1. Tsukuyomi was never an option from the last battle we saw, thus give us a hint that itachi might know it wont work(he's smart after all, you said that urself). Sound based genjutsu is not the same as visual genjutsu. As ma and pa frog said, their sound genjutsu is their strongest genjutsu attack. So thinking if one attack works why wont the other is a fail.
2. If there is one attack of itachi that is completely useless against nagato its Amaterasu. Why? we all saw how he repelled the fire by shinra tensei, and everyone will agree that since its a ninjutsu it can be absorb by preta path. again, itachi is wise that he did not use amaterasu to attack nagato the second time coz he already know it wont work.
3. Totsuka sword is the only way itachi can beat nagato honestly. but this one is still debatable coz nagato will not easily fall for a cheapshot if its one on one and he is focused fighting itachi and not taking 3 most powerful ninja. It can be shinra tensei'd, susanoo itself is vulnerable to chibaku tensei.
4. Yata mirror cannot block any attack, its vulnerable to banshou tenin,shinra tensei and chibaku tensei. If you think with sense, how can a shield block a non projectile attack like chibaku? it will just be pulled right in the center with susanoo and eventually squished. Again, Itachi did not use yata mirror to chibaku tensei coz itachi is much wiser than you that he knows yata mirror CANNOT block chibaku tensei.. not to mention, its a chakra thus can be absorb by preta path.bad news for you huh?
5. LOL, the magatama, why itachi fanboys always exaggerate things? that long range attack of itachi can't destroy chibaku tensei alone, itachi is WISE he knew he cannot destroy it himself that is why he ask for it, as simple as that dude. Again itachi is smart he knew even if he hit the core repeatedly its just a waste, do you actually believe magatama is stronger than TBB and Naruto's rasenshuriken?! lol clearly a hardcore itachi fanboy.
*using 3 magatama to break chibaku is just dumb dude and doesn't sound like itachi,he'll ran out of chakra plus he might got squished before he can fire 3 magatamas. I repeat, itachi is smart, he knows exactly what to do in that shituation he cant afford to waste any time or else they're doomed.
6. lastly, coming right from you itachi is smart. HE knew he cannot take nagato alone, that is why he let naruto and bee fight nagato first in order to think and come up with a plan. If he knew he can take nagato alone, he should have said to naruto that just to go on and leave nagato to him. Logical isn't it?