I noticed a similar issue with my 04 LeSabre on doing the mounts.
I got mine from Rock Auto. My front mount was totally trashed, and I installed the new one. All of a sudden now I have engine vibrations that can get pretty bad. It has softened up a little with some use, so I tend not to notice as much any more.
I also got a rear trans mount at the same time, same manufacturer. And it is made in Taiwan. No kidding. It looks pretty solid, actually, but its probably too stiff a durometer of rubber, hence why I was having problems with the front mount and vibrations. I didn't install the rear one, but it looks like a lot less material to absorb vibration that a factory GM part. So you are on to something with that. I'll bet yours are probably china or taiwan made as well. It may bolt up right, and do what it is supposed to do, but the softer cushy rubber mounts that are factory originals probably provide more cushion than the cheap and inflexible rubber aftermarket ones.
2004 Buick LeSabre Custom FE5 GXP suspension conversion. 170Kmi
2001 Silverado 4WD 5.3L, 33" BFG ATs, Z71/Z82 pkg, 147kmi.