I find it funny that everybody is ripping on the OP claiming he hasn't read the manga; however, nobody has yet to show a single manga page that shows Tsunade with Hashirama.
As for the whole argument of "Hashirama said he taught Tsunade how to gamble," that happens to be what the OP is claiming to be a chronological inconsistency. So using that as supporting evidence is pointless.
Now, I do have problems with one of the OP's arguments. Specifically, saying too much would have to happen in a 3-4 year period. Take a look at what has occurred in the past 3-4 years:
1) Tsunade's entire reign as Hokage occurred, including her time in a coma (yes, I'm assuming her being cut in half will end her reign).
2) Jiraiya died
3) Orochimaru was sealed
4) Orochimaru was brought back
5) The 4th great shinobi war occurred and is close to conclusion (total start to finish most likely < 1 year)
6) The entire Akatsuki organization was wiped out (remember, tobi was a replacement)
7) Konoha was destroyed
8) Konoha was rebuilt
9) Danzo's entire reign as de facto Hokage occured
10) Naruto completed the rasengan by infusing it with elemental chakra (something Minato was unable to achieve)
11) Naruto has befriended the kyuubi and become a perfect jinchiruki
12) The jyuubi was resurrected.