I can't offer much regarding the 61, I'm only just familiarizing myself with the 63 and later gm truck 12 bolt, but I can say that for the 12 bolt job you do need to pull the carrier, then the pinion out of the housing to get to the pinion bearing, if memory of the shop manual serves correctly. So yeah, gears gotta come out, full-on deconstruction of that rear end.
I'm rebuilding the original from my 64 now, and I've got everything stripped out of the housing with the exception of that pinion, and I plan to tackle it this weekend. Normally you'd need a press to get the bearing off the pinion gear, but I can't say if that's always the case with a shot pinion bearing. Mine's shot so I'll let ya know.
Yours may well be shot too, that wonky driveshaft prolly did a number on it. When mine went, the pinion gear slid out and ground into the carrier, basically leaving the rear in need of a full overhaul. So I took the quickest, cheapest route and swapped in a 69 12 bolt I found on craigslist for $75. For the 61, you may be looking at some custom fab-work to get your trac bar right and all that, but a full rear end swap is prolly your friendliest option.
As a side note, I'll try to keep track of everything I'm doing with my 64 12 bolt build-up and work it into another thread or a tech article for everyone.
Paul