Vibration After Stop Accelerating the Throttle at or over 80 miles per hour

If engine is shaking check those mounts as said above, the harmonic balancer was set up at factory and would have to be damaged in some way, but you could still put under drive pulleys on and gain a few hp if you wanted to get another mod under your belt. If the vibration occurs without any obvious sound then do the simple first and thats the balancing, may try out some wheels and tires from another stang to verify.

I tried placing my stock wheels, and the vibration is still there...

Tie-rods, ball joints, rotors, Some fords have cheap plastic parts like the cylinders or mounting hardware on/in calipers, brake pads crystallizing or too tight and wheel / Hub bearings & seats or loose parts and mounting hardware or uneven alignments. Unbalanced or bent drive shaft. Axles in rear end may have issues with bearings & seats or bends, control arms may be bent or bad bushings. Shock bushing and mounting hardware or loose, sway bar links and bushings worn or too tight or too loose. A weak coil spring. Front end alignment out or camber & toe too far out or in not letting the full tire tread stay on the ground. Tune up parts air filter clogged bad spark plug or wire causing rough engine shake. Rear end bolts loose If its never been wrecked you can look over a bent frame for the cause but these are just a few extra ideas I had. I know you said a mechanic will have to locate it but they may not be in a mind to locate without trying new parts until its found and all the work already done to it needs looked at again to be sure there is not something wrong or over looked there too.