I ran a 79 Bonne back in the day. Mine was a 350 as well, but it was a BUICK 350. I too lost the head gasket shortly after it cleared 100k. I think we need to determine which 350 you have before we can get you an accurate assessment on your swapping question. You could have a Pontiac, Buick, Chevy or an Olds V8 equipped car. GM was notorious for these types of engine installs under their new-at-that-time "Corporate" drivetrains. The LT1 could be swapped in, but it would be labor intensive due to the reverse flow cooling orientation. One would need to check for motor mount compatibility as well. The transmission is more than likely a 200R4 if it came out of an 84 Monte. The 700R4 was never available in the G-body platform. A 700R4 is a bolt in because it was offered in the 80'* vintage B-Bodies. All you would need is the trans crossmember/driveshaft and some other odds/ends for the transplant. The rear end is a no go. You might be able to pirate the guts, but a 94-96 Impala SS or 9C1 (police pkg) would be a better choice. The G-Body diffs are too small in width and their mounts are not compatible with the B-Bodies. I hope this sheds some light.
2000 SSEi Galaxy Silver...All the toys: K&N,Gutted A/B, Mobil1.
2002 Monte Carlo SS: K&N, ZZP DP, Mobil1.
2001 Suburban 2500: 496 BBC K&N, Mobil1