The MK3 uses a combination of unibody and subframes.
In my opinion, the best way to reduce the weight of the MK3 is to turn up the boost pressure and add more fuel. (IE: not even bother. (LOL)
If you must cut and add pipe, your likely going to end up with a less effective structure than Toyota designed from the start. The only way your going to get a stronger strutcture is to add braces across areas that normally did not have them from the factory, and that is going to compromise your use of the car. (Like having those bars across your cargo area, or going along the belt line from the A to C post.) Sure you can make any vehicle stronger, but it's all a trade off of use v/s structure. Notice the NASCAR guys don't have doors? Neither do most small track race cars. They weld them shut and add outside bash bars.
I have thought about adding ladder type subframe connectors to the MK3. (They would be attached to the underside of the floor on both sides at the rocker pinch welds, and also to the sides of the exhaust/driveline tunnel. The tunnel will have "hoops" sectioned into the floor to further make it stronger too. Bolt in driveline hoops to close the "circle" would complete the structure and allow you to work on the car still.)
What we used to do when I built limo's was to weld metal straps across the floor pan of the stretched area. This was in conjunction with new crossmembers to hold up the extended multi piece driveline, and carrier bearings. It is pretty amazing how much stronger the floor can be made by just adding a web/gusset pattern to the existing floor pan of 1/8" x 1" cold rolled steel strap. You stitch weld the strap to the floor, and use a hammer to help keep it formed to the contours of the existing floor. Tie that to the subframe and it would make the MK3 very resistant to bending which is the problem you feel with the targa top off. (Start with a hardtop car, and your 100% better off to begin with if your going for the ultimate handling MK3.)
The down side is added weight to the car, and the noise your going to hear from the subframes being "welded to the car" at the points where you have them connected to your unibody/ladder frame. (The stock rear subframe is rubber isolated, but the front one is directly bolted to the unibody, so isolation there is not an issue.)
If you modified the rear subframe so it could never be removed again, you might be able to remove some weight at the brackets that mount the rubber isolators, and replace it all with tubing and brackets welded directly to the unibody, and tie them into some carefully placed crossmembers to make the struture even stronger at the expense of some limited loss of cargo space. (Think X brace going from the wheel houses to the inside of the roof/quarter sail/C post area.) If you did that behind the rear seats, you could maintain passenger space, yet still have a very strong design.
The "free" way to also improve your cars structure is to "seam" or stitch weld where the factory seams in the car are. Keep in mind, when you do this, you make the car less likely to bend, but that is BAD thing forward of the front strut towers, and rear of the rear ones. You also have to remove all the seam sealer, and then replace it when your done if you want to keep your car wet weather useable.
So, to keep weight down, a combination of the following might work out, but it would be ALOT of work.
1) Strip the interior, seam sealer, undercoating and other flamable stuff on the car. (Sound deadening etc.)
2) Seam weld everything between the strut towers.
3) Using strap, reinforce an X brace that ties the tourqe boxes together across the floor pan. (Goes up and over the tunnel etc.)
4) Using pipe, weld in a rear "doLuck" brace behind the front seats.
5) Using strap, do the same across the front of the floor at the floor to cowl point. (Completing the "box with an X across it.) The quarter rails are the other sides of the box...
6) Fabricate ladder frames for each side that are welded into the floor at the main pinch welds along the rockers, they would further be cross braced too. These are tied with strap through the floor to the improvements inside the car. (Welded up where it passes through the floor so no seam sealer is needed, and it's as strong as possible. You could even use short pipes, and a hole saw if you want, but the strap placed right would do the job fine, and slots to pass the strap through are easy to cut with a small die grinder and cutting wheel.)
7) Fabricate an engine bay brace that ties the strut towers to the cowl.
8) Fabricate a new subframe brace that uses the stock bolt in one, and the "doLuck" brace that bolts to the lower control arm rear points. This could be X'd to be even stronger too.
9) X brace the rear cargo area, from wheelhouse/foor edge to C post/roof area.
10) Strap or pipe across the underside of the roof to tie the X" tops together. Personally, I think using strap there would work fine, and maintain a low profile to keep your rear view as open as possible. Same with adding more structure to the sides along the inner parts of the C post, using strap there is a easy way to make it stronger, and not lose much passenger space. (Straps could be angled up from the "doLuck" point at the rear tourqe box to the attachement point of the top of the cargo area X making the car that much stronger w/o much loss of interior space.)
If you did this all right, the interior trim would even fit back into the car most likely, but you'd have some holes needed for the X brace to pass through. This cage would not be NHRA leagal, but it would be stronger in any type off crash, and maintains the factory crush zones forward and aft of the strut towers. (Which saves your life in a crash by absorbing some of the energy v/s letting you stop to quickly and die.)
When your done with all the additions and welding, you can further make the car stronger by filling all the boxed channels with two part foam.
Good luck.
