thanks for the compliment xd props to you also for using logic and not hype as well, which is also the norm when it comes to dojutsu.
i'm not saying the summons are useless, but minato with his speed can almost ignore them. the dog is probably the strongest summon in the series, after gedo mazo, and pretty much indestructible, but not all that fast. the crab is tricky too, but i doubt he can cover all of what's left of konoha, minato can simply change location. although he could limit the use of minato's kunai markers. as to the bird, yeah the paths can use it to fly, but then they can't attack xd except for the larger scale shinra tensei. and the summons are taken care of if the animal path is defeated.
i'm not sure about the rasengan, naruto did remove the chakra rods from the deva true, but the other paths hit by the rasengan (animal and the reviving) weren't restored... it seems to be enough to incapacitate them for the length of a battle at least. and minato does have other low tech options like decapitation, removing the chakra rods or their eyes too.
to be fair, pain starts at an overwhelming advantage, minato has to figure out each pain's ability, and nagato has a much wider and more powerful range of jutsu. And i'm almost sure that Nagato will survive, it's possible that minato can figure out that there's someone controlling the pains but given that it took an entire village plus jiraiya's inside knowledge ages to figure it out, it's too much to assume. so even if Minato defeats the pains, Nagato can still make more. But, it's been shown that the linked vision can be overcome with speed (jiraiya blinding one pain with a kick), so it's not impossible for minato to win.