No, you said "3sgte is a heavy motor also", which it is (not by much).
My car has no issues with the extra weight adding the fact that piping was fabricated in steel and not the light stuff plus running a 3037 with an external gate and the bigger 2.3896 crank.
I swear the handling feels like it has improved, you go fast into a curve and the front just tucks in and neutral oversteers (not much).
Maybe you had issues because of the way the weight was being distributed, I have seen a 13bt ae86 with the engine mounts fabricated to front of the chassis, that means all the weight will be distributed next to radiator which cause nose dive, the steering was super heavy and the front wonders on full boost
I made custom mounts to bolt were the 4ac bolts too (front crossmember) and the same mounts for the staz gearbox, no problems.