I commend your prudence with your daughters safety!
I'm not to that point (with my car or my daughter) yet, but here are a few quick brainstorm* ideas. If there isn't a forward facing 'harness booster' seat that will fit in the race seat, I would consider devising a setup that interchanges with it. I'm thinking a frame that bolts to the seat mounting holes, a lap belt strap to secure the base of the 'harness booster' with, and a sheet metal pan to hold some seat foam below and behind to mimic a typical installation. Or maybe instead of the lap belt securing the 'harness booster' base, go with a standard high-back booster, and assuming your harness has 3" wide straps, swap it out for a 2" strap harness that is fed through the booster. Finally, and potentially least desirable from a safety perspective, it might be possible to find a backless booster that fits in the race seat, plus some creative use of foams (like styrofoam plus a little something firm but compressible for supportive comfort) to fill the gaps, and again going to a 2" strap harness.
* These are only ideas. The idea generator may not be held liable for any fault found with said ideas. They may not even be safe, or legal, in principle and/or execution. Use or incorporate any part of them at your own risk.