if you think about it, you take the top off, then open the two doors. your whole car is being held together by whatever is on the bottom. the leverage alone is going to give you flexing. in future designs, toyota stiffened up the frame, the windsheild and rear window supports so the mk4 with the tops off is as tight as a mk3 with the top on. the mk4 still has targa shimmy. it is physics, and you can't beat science!
we have these various options.
add the front and/or rear strut tower bars. these provide a fair amount of stiffness as it creates a box around the suspension.
aftermarket sway bars also help to tie the sides of the car together, but do help a little.
stiffening up the suspension will not help stop the targa sway, as stated earlier, and will make it worse as the suspension passes the bumps off on the rest of the car.
Reg in calgary and a couple of fellows have fabricated targa-bars which connect up to the 4 bolt holes for the targa, but still allow that open air feeling. think of it as the biggest sun roof you have ever seen on a supra. these get you as close to having tha targa on as you can get, as long as you get them from reputable people. i heard of a few guys who made bad ones which didn't connect all that well, or provide the required stiffness.
thats my 2 cents. i don't often look in this section. if you have any other supra specific questions, feel free to PM me or post it in the supra section. I frequent the supra section, and the meets, and occasionally the off-topic. okay, okay, off-topic is where i heard to first every night looking for asian pron!!!!