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My 94 LT1 breaks a little to the right on acceleration. Never to the left. Of course your engine has more cubes.
I would take it to a good alignment shop or a good mechanic and drive it easier till you find the answer.
Any one of a number of suspension issues could be causing this. Your 94's suspension is now 16 years old, and the bushings (if original) are probably either rock hard or have turned to mush, probably the latter. Check the following...if needed, replace with poly and lube generously with silicone grease.
Batwing bushings
Trailing arm bushings
Strut rod bushings
Sway bar bushings
Rear tie rod assembly (toe link) and ends.
Check for any play and replace parts as needed, finish off with 4 wheel alignment. That should cure the problem.