Am I just SOL?

Reduce unsprung weight, improve handling.

That unsprung weight is literally at the roll center of the car so the effect on handling is negligible. If that's really the concern get some aluminum 17-18" wheels and 35-40 series tires, way more bang for the buck in reducing unsprung weight in a useful way. Also it'll be a massive improvement in handling and steering feel and response over 15" steel wheels with fat mushy 60-series street cruising radials. I know because I've run both setups lol.