IMO, moving the engine 1" up down, forward or back, is going to require cutting and welding. The question is actually is there less cutting and welding by moving the engine than opening up the trans tunnel. I'd say it depends on your expertise. Of course with a '71 Cuda, value impact of those mods and the ability to reverse them could also be a factor. Plus you have a shaker, so you not get another layer of complexity to making it work correctly.

FWIW, I did lift my small block .5" up in my E body's engine bay using spacers in between the engine mounts and isolators. Theory being by lifting the engine, I can now drop the car down lower. Engine weighs 500#, the rest of the car weighs 3000# Which has a greater impact on COG weight? IMO, by moving you engine forward an inch, you negate any handling gain you would have by dropping it an inch.