I belive the targa v/s non targa cars are more of a difference than the "official" numbers to be sure. (Toyota admitted that in the intrest of safety and long term strutural reliability, they over built the Supra, especially the Targa version. This was from the guy in charge of design, in a Car and Driver article from the 80's.)
Mine weighed in with me in it, and two boxes of tools at just over 3800lbs a few years ago. (Stock 88T 5speed Targa.)
If I was going to build up the lightest MK3, start with a non ABS, Non TEMS hardtop NA. Remove everything but the seats, plexiglas the quarters, speed hole drill out the unibody where possible, and then foam what's left to try and keep it strong enough. There is lots of metal you can remove in the inner door shells, inner rockers, crossmembers and other places you can get to with a hole saw. Just be carefull and don't make the car so weak it's going to kill you in a crash. (I'd only go wild if I added a cage into this structure, then removed much of the extra metal in places where it will not create leaks, or obvious structure problems.)
I bet you could get a MK3 under 3000lbs with the right mods, even with a cage. But, it would not be a car you'd want to drive more than across town with in the end.
Far less work to just add more power, and keep the luxury and sound deadening in my opinion.