TAKE IT OUT OF FIRST GEAR DUMMY!!!
Seriously, If all you did was change gears, then I can't see how this alone would do it. I have changed many gears in these rear ends and never had this problem.
maybe 1)pinion preload is incorrect(you said it was)
2)driveshaft was banged/weight knocked off.(you said you balanced it).
3)there was a balance problem before but you never noticed because you didn't drive at the rpm you do now(steady rpm in any gear causes vibe or just speed related?)
4)tires(why would they go out of balance during the gear change? you said you balanced them though)
5)pinion bearings loose/worn(you DID put new bearings/seals in RIGHT?)