I have an LT1 (I know, not exactly the same but still a non gen 1 fuel injected engine) going in my '35 and there have been a few small things to overcome, but nothing terrible. The LT1 has a better sounding exhaust note than an LSX, the engine doesn't look like plastic and you don't have to deal with things like coil pack relocation and stuff like that. My 06 GTO also has an LS2 and it makes for a great daily driver. By now the LS engines have been out going on 15 years and the aftermarket support for swaps makes things quite a bit less painful. A new engine harness for my LT1 would have cost $750, but I had my stock harness cleaned up by LT1 wiring (they do all late model GM stuff) for half that. It will likely cost more to build, but the end result will be will worth it imo especially since you say you are building a daily driver.

I say go for it!