I'm bit late on commenting on this, but I must say, I love it. You definitely seem to have put a lot of work into this! Anyways, to begin with, obviously, this is all about match-ups. If it were a 10 vs 10 scenario, it would be impossible to actually judge the winner. So seeing it that way, I think you're title is a bit misleading, in that you just seemed to have found match-ups that would be in an overall way favorable for Akatsuki (but I still think you may have gotten some wrong). I'll go through your match-ups now 1 by 1, and give my comments on them.
1. Itachi vs the Second Tsuchikage
You only mentioned how Itachi could win, which is in general how he could win against anyone.
Muu has many things going for him here that could easily provide him with a win.
If he can create a jinton large enough to envelope Itachi's Susanoo, he could easily win. As seen by how Oonoki enveloped 25 Susanoos and none escaped, it can be inferred that Itachi would also not be able to escape, and his shield would be unable to protect all of Itachi. Also, his invisibility would allow him to sneak up on Itachi to the point where he can easily capture him in a massive jinton. I don't think that Itachi's sharingan would be able to sense him seeing as he can erase his chakra signature, which SHOULD mean that this attack should work. Barring that, With Muu's ability to fly, he could avoid the Sword of Totsuka. Really, the main problem is Amaterasu, which, granted, if it hits, then it would be difficult to deal with, and it may force Muu to split. However, Muu's earth techniques could also form a barrier between himself and Itachi, which would drastically lower the effectiveness of Amaterasu, and Muu's sensing abilities would certainly provide him with a warning that Itachi was about to attack. Itachi's genjutsu could also be a major problem, but Muu, having dealt with Genjutsu in the past (fight with 2nd Mizukage) would certainly be wary of it, and his sensing abilities would also be useful here.
Overall, I think that this is actually much more of an even battle, with Muu having the ability to sneak unnoticed around Itachi and envelope him early. If that doesn't work, then Muu still has still a very equal chance of winning. I'll still say it's more in favor of Muu as a matter of fact. 50-55/100 times Muu wins.
2. Kisame vs 2nd Hokage
From what we know, Kisame should definitely take this, but of course, we know next to nothing about the 2nd, and with more knowledge that could easily change. We don't know about his space-time, or what his edo's were like, or even what made it imperfect. I know however that you had to add him in, because you had to find 10 (you should have kept A. Just because he's a replica of his dad doesn't mean that he would be a hindrance, and you could at least argue for him more easily).
3. Hidan vs 5th Mizukage
I do believe that you are wrong here. Mei's style is wide range powerful attacks, which means that off the bat, Hidan would be at a disadvantage because he would have no way of getting close to her. And just because he can't die, doesn't mean he can't be rendered useless in battle. And considering Mei's jutsus can certainly maim him (she could MELT him, don't know how he continues fighting after that), she certainly should take it. Immoratality is just the inability to die, it doesn't render her techniques completely ineffective. Mei wins 80/100 times.
4. Deidara vs Minato
Minato should in every way dominate Deidara. FTG allows him to easily avoid attacks, and his barrier would allow him to escape the big ones. I think his barrier is the key to taking out C4, as it could warp away the mini bombs as well. FTG level 2 coupled with his inteligence could be used against Deidara if he takes flight. And to avoid Deidara's suicide bomb, Minato could do what Sasuke did, and reverse summon himself to safety using his frog summons. So in effect, Minato wins. (And we don't even know everything about Minato eg: his chakra affinities. We know he has them, because he created rasengan with the sole purpose of combining it with an element. He could also have more levels of FTG for all we know). Minato wins 70/100 times to me.
5. Kakuzu vs Second Mizukage
Here I think you are underestimating the Mizukage's genjutsu. He should certainly be able to use it, as he summons it at the beginning of his fight. And Kakuzu would not know that he is under a genjutsu (the only reason the army did is because the Mizukage TOLD them), so he would only attack the mirage, rather than having his hearts attack all over the place. This would also allow the Mizukage to use powerful jutsus such as joki boy to take out Kakuzu's hearts. He might not destroy the main body, but he could certainly destroy many of the weaker hearts during the mirage phase. If Kakuzu finds out he is in a genjutsu and somehow manages to destroy the clam, he will already have been weakened, and the battle will be a lot more difficult. Seeing how in all probability, the only heart able to survive joki boy would be his main one (with it's chrystalization) it would be a much closer battle. And since even still he should have weak spots (mouth and eyes), and he has no real way of killing the Mizukage (intangibility) the Mizukage here should also have the advantage. I say Mizukage wins the majority of the time, although it's close, because Kakuzu has much battle experience that could allow him to figure out the genjutsu sooner. Mizukage, 55/100 times.
6. I agree with Sasori winning this, his ability to repair his natural puppet form would allow him to avoid the Kazekage's main attacks, and one hit against the Kazekage = the end, which Sasori could do with a majority of surprise attacks. However, the Kazekage could use something like Gaara's sphere, which would render Sasori's attacks useless overall. But he still has no real way of KILLING Sasori, and so overall, you're right that Sasori takes this. Sasori, 75/100 times.
7. Zetsu vs Gaara
I think Gaara should take this. If Zetsu plants chakra spores on Zetsu, he could certainly pull them off like Oonoki's assistant did at the summit. Also, if he is wearing his protective barrier of sand over his skin, he can simply dispel it to get rid of the chakra sucker. If Zetsu were to create Gaara clones, they would be far weaker, and he himself must have a chakra limit, so he can't make too many also. Their weakness, coupled with Gaara's knowledge of his own techniques, should allow him to defeat his clones.
Gaara's ability to fly would make it very difficult for Zetsu to reach Gaara in the first place, which would make it nearly impossible to plant the spores. And the fact that Zetsu can merge with the ground to travel seems like a problem, but seeing as how Gaara can control the terrain itself by turning the ground to sand, he could lift the ground up altogether, and trap Zetsu within it.
Overall, Gaara should certainly have the upper hand, and I would say he wins 70/100 times, but mostly due to him seeming to be a bad match-up for Zetsu. However, our lack of knowledge about Zetsu overall, especially Black Zetsu, allows this result to change with more information.
8. Konan vs Oonoki
After reading your analysis on Konan, I realized that I have been underestimating her, even while telling people that they were underestimating her! She has a very good chance here.
She could definitely avoid jinton by splitting, so I think her main worry would be his fire techniques. However, if she soaks herself as you say, then she could definitely take the upper hand. If she merges her paper into the terrain, she could surprise Oonoki as well if he's not flying. If he is, however, it would be very difficult to capture him, and so she may have to resort to her suicide technique.
A way for Oonoki to win would be to increase the weight of her paper (remember, he also has the ability to alter the weight of a target). He could do this if she binds him, which would allow him to escape because the paper would be to heavy to stay on Oonoki. It would also serve to slow down Konan, which would make it easier for Oonoki to hit her with jinton.
Overall, this battle would be very close, and I actually think that it could go entirely either way. 50/100 to either.
9. Nagato vs. Hiruzen
I do not believe Hiruzen would EVER reach Nagato to be able to use the Reaper Death Seal. From what we've seen from Hiruzen (hype is useless here), there is NO way that he wins. Obviously we don't know his prime, but until then, Nagato wins 99/100 times (this is being nice to Hiruzen).
10. Tobi vs Third Raikage
The problem here is obviously whether or not the Raikage is fast enough to hit Tobi. If he is, the chances of his victory skyrocket massively. We do know that the Third Raikage was faster than A, so the chances are actually pretty good. So I'll split this into 2 scenarios.
A (Raikage is fast enough to hit Tobi): If this is the case, then Tobi's only chance is genjutsu. We know that his is powerful, considering that he could control the 9 tails with a 3 tomo version. But the Raikage could avoid eye contact, and seeing that he, being a kage, should be wary of genjutsu, it is a possibility that he does this, or that Tobi doesn't have the time to activate a genjutsu if he does due to his speed. If Tobi can't trap him, then the Raikage's ability to hit him means he's dead. In this scenario, the Raikage wins 80/100 times.
B (Raikage isn't fast enough): If Tobi can still evade the Raikage's attacks, then the only problem would be figuring out how to kill him. Genjutsu would work, and he may even figure out to make the Raikage hit himself. The Raikage's only chance is to wear out Tobi with his massive endurance so that Tobi slips up, and not get caught in any trap. But overall, Tobi here has a massive advantage. In this scenario, Tobi wins 90/100 times.
So that is my overall analysis of your analysis. I think that you underestimated the Kages in many instances, I see it being more in favor of the Kages than Akatsuki personally. However, that is only in these specific scenario's, obviously in a 10 vs 10 scenario (which is the only real way to figure this out) it would be different, but that is impossible to figure out. And obviously there are tons more matchups that could take place which would yield different results. And obviously leaving out Hashirama is huge for Akatsuki. But, still, nice thread, I had fun commenting