I was using some West System epoxy to demonstrate boat and RV repairs, and that stuff is amazing. (There is a filler that looks like little fuzzy cotton balls, and when you add it to the epoxy, it becomes like mayonaise and stays where you put it. (It does not expand however.) When cured, it's harder than the substrate material on many boats. (Wood.)
I wonder if they make an expanding foam in this stuff. I'll have to check, but like the 3M stuff, it's not cheap by any means.
The Ford foam is in the A posts, and it's heat expanded. (Expands when the unitized truck cab is baked after being e-coated.)
I belive the weight difference between the higher PSI two part foam and the lower PSI ones is pretty minimal compared to what your getting structure wise. The foam alone is not that strong IIRC, but it's ability to keep the metal that's around it in place under load is what improves the overall effect on your chassis. (Seriously reduces flex as the boxed areas become very resistant to being twisted or bowed in any direction.)
One thing I would NOT do is add any foam ahead of the strut towers, or behind the rear towers. (The upper location point of the struts.) These areas are designed to crush in a controlled manner that slows you down just right so your brain and internal organs don't get slammed into your skull or ribs and kill you. Filled with this foam, they would not crush right, and it's going to allow more energy transfer into you and other occupants of the Supra.
I would think filling the front and rear cradles/subframes would be a good idea. Steam cleaing them first is totally needed. Oiled metal does not allow for a good bond between the foam and the subframe ID. (possibly why that car creaked IJ? I'm just guessing, but that's a common problem. Especially if the car was Z-barted or had extra corrosion resistance sprayed into the panels. That stuff is waxy, tough to remove and is a problem when repairs to the rail are needed. The only good news is it's somewhat resiliant, and will self heal sometimes if the surface is only scratched.