The next part of your theory states that Hashirama was killed by a worthy adversary. I can't remember if ever mentioned or not in the manga but I believe it was never revealed just how Hashirama died. So saying he was killed at all may not be an accurate statement since we've seen on several occasions young deaths for various reasons other than being killed.
For a few reasons I don't believe Madara ever fought Hashirama a second time. For one reason if Hashirama and Madara's fight was so legendary before and so devestating to the land, I have a hard time believing the two fought again without some knowledge by other shinobi. They created the Valley of Ends when they last fought (their suspected last fight) and their story went down in history as one of the greatest battles. It changed the maps basically. I don't believe a second fight would be any different, especially if Madara had the Rinningan and Hashirama was brought back as an Edo Tensai summon with unlimited stores of chakra, and if Tobirama was assisting in the battle. A second battle between those two monsterously powerful shinobi is something that would've been known. A third time? Definately not, though that's my opinion. I feel there'd be a few less countries if those two fought again xd
You then go onto say something that somewhat contradicts the whole technique of Edo Tensai. You first say that not all souls go to the pure realm (which I believe with White Fang). You say if Madara defeated Hashirama a second time, that his soul may not go to the pure realm or rest in peace, then how might his soul be ressurected? The technique's description given by Kabuto which hasn't been challenged either here nor anywhere else, that the souls are taken from the pure world and brought to the impure world. If Hashirama had regrets or feelings that prevented him from passing peacefully, how could Tobirama have brought him back? And if Hashirama's soul had been released from the Edo Tensai in the say of Sai's brother or some whre he was finally at rest, then how could Orochimaru come back and summon him?
The latter question comes from my own belief that if a soul is brought back by Edo Tensai and then comes to terms to unroot themselfs from the earthly binds of the jutsu, then essentially they can't be brought back. The validity of this isn't proven nor do I think will be but it's not disproven.
