In this day and age alot is possible. The muscle cars do lend themselves to being more dimensionally adaptable to the nbs chassis and track width etc. Length is easily changed by cutting down or lengthening the chassis. I would suggest to change the rear 5 link to a triangulated 4 link or 3 link. Only reason I say that is the rear lower control arm mounts are pretty low under the rest of the chassis, main reason I mention this is the ride height of your car needs to be low and aggressive for sure. The other thing that may be a hurdle is the frame height vs the unibody car, You will be channeling alot of steel into the interior, estimate about 5" to tuck most of the frame under the rockers. So this can cut down on seat height and comfort. If your not a tall or big guy then then you may be perfect in this setup.
I always consider all aspects of a build before jumping in.
If you're really handy with a welder, you could make a cut out of the top of the chassis just under the front seat for additional height and foot room. Just have to add in some steel on the sides and maybe another cross member.
Ive done some s10 chassis under 50s trucks and they fit well. I'd be interested in seeing what you're starting with.
I think the positive of doing a swap like that is suspension and chassis support in aftermarket is really good and cheaper than the mopar stuff. I am guessing your keeping the LS platform and is main reason for the idea behind the swap?