Can the entire engine and transmission from an LT1, LS1, LS2, etc.. be swapped in place of the stock VX system, then just mod/connect a drive shaft to the rear axle?
Yes! The NV4500(heavy duty manual transmission) and an NP205 transfer case is actually a couple inches shorter than stock. At worst you may have to have the driveshafts modded/manufactured/etc. Most VX's would even be overkill with an NV3500 which IIRC is the same size and much more available. I don't know anything about auto transmissions though, so you'll have to do your own homework there.

Space is the issue & Wisdom can probably answer that question best. Considering he didn't have enough space to mount an AC compressor with a 5.3L V8, I would think a 6.0L LS2 might be a bit too big.
All the LS series motors are the same exterior size with the later engines being only slightly larger on the heads and intake manifold. A/C can be done with a relocation kit or by changing the accessory drive configuration. There are also many options used by classic hot rodders to have A/C in vehicles that never came with it.

Will our rear axle be ok with direct feed from a LS*'d Chevy transmission?
Yes. They have been compared with GM 14 bolts and Dana 60s which are both heavy truck axles.

Emissions laws SUCK!

If you are looking into engine swaps, check your emissions laws first!
So far, it's a no-go for me. (luckily I found out before I bought the donor engine/trans).

I was doing some research and saw that Ascinder was having a forum conversation about this subject on Pirate4x4.com. Hopefully he reads this and has some more info/better news.
(sending him a PM too...)
Sorry, haven't been able to find out anything more, except you may check other counties. Some have smog here and some don't. Your mileage may vary....