Some thoughts.
There has been no change in Bilstein Sport units for the MKIV in years. I bought several sets this year and all are the same as ones bought ten or more years ago. Possible issues that come to mind. Incorrect seat castings supplied. (Unlikely, check the casting numbers on them). Front / rear springs mixed up. (Seen this before). Tired springs that have taken a set. (NEVER seen this with Supra stock springs).
Bilstein Sports used with stock springs lower the car the car front and rear between 10 and 15mm. A spring seat 10 mm lower does NOT lower the car by 10mm. It lowers it the geometric ratio of the bottom arm length from inner bush to outer ball joint relative to the damper mount hole in the arm. The ratio is different front to rear. A ruler on a bottom wishbone or rear lower arm, preferably off the car, will give you that ratio. I can't remember it without referring to my notes.
Re gassing Bilsteins needs a specialist muffle jig, although I have converted them to a Schraedar valve in the past.
You need to machine new circlip grooves, not use a spacer, the circlip retention depends on the seat encompassing the clip. I machine new grooves all the time for custom set ups.
Finally I *THINK* if you use Soarer springs on the Supra Bilstein Sport dampers you get the effect you are discussing. The best tech advice comes from Bilstein themselves in Germany, but the tech guys mainly only speak German.
Some generic fitting reading: https://www.bilstein.com/uk/en/blog/watch-avoid-installation-mistakes/
Some interesting reading on suspension technology generally implemented after the MKIV production life: https://www.zf.com/master/media/en/corporate/m.../dmpfungsmodulefrpkw.pdf
Finally, having to have Bilstein machine grooves at different heights to use a supposedly stock MKIV TT spring set on stock Bilstein Sport dampers smells extremely fishy to me, I think the real issue has not really been discovered here.