True sorry.
I believe there are much better candidates to use for a LS swap than a MKIII. I am against a V8 swap into a MKIII unless it is a 1UZ, but if OP wants to do it, it is his car. I would just like to see the outcome (build thread). I believe the I6 motors have enough potential for OP's goals (not knowing what they are, but just guessing they are about the same as most MKIII guys). The LS swap would be pretty unique tho, but also a challenge.
Back on topic.
OP your best bet is to find a shell/parts car, especially if you want a targa that bad. They are cool as hell, plus the ladies love them, but the down side is that they have no where near the durability of a hard top. Even with my car 100% stock I remember I had the targa wiggle bad, I also only had 7x,xxx miles on it when I got it so it, so it should still have been really strong.
If you do end up going this route, a parts car or a rolling chassis would really be the best bet for you, as it would all be there, and you would not have to try to fabricate a targa top, and bracing out of a non targa car. Also without the bracing they add on to the targa cars, I could not imagine how bad the chassis would flex.