Who here has run a suspension that was too firm it made them feel "unsafe" on turns?
The Baja's suspension was too stiff (as a whole)for most of the tires I was running on it. It was probably too stiff in general, I had to run harnesses to stop my head from hitting the ceiling. When your car is bouncing enough to unload the tires, it's a) slower and b) less safe.
Wagonzilla was the same thing once I went to coilovers. Switching to a more serious summer tire helped a lot. Sidewall flex and grip level worked with the suspension nicely. My current coilovers are softer and actually have a progressive-rate spring in the rear which calms the back down some more. The price for stepping up to big boy tires tends to be high: road noise, not the best wet performance, and expensive.
My IS300's suspension was too soft for the 225-45-17's I had on it, switching to 16's on mid-tier summer tires matched the suspension much better. 16" small-car-tire options, as you said, are dwindling. Mine were the Dunlop Direzza DZ101's, the predecessor to the same tires I'm using on the Mazda (DZ102's).
My Legacy's suspension was too soft AND too low with KYB GR2's and Tien S-Techs. Hitting the bump stops does effectively the same thing as having a way overdamped and oversprung coilover. going to WBM 2007, I hit a lane-wide pothole or mis-aligned expansion joint, got a bone-jarring slam through the whole car. It then launched off the bump stops, and skittered across the road 8 or 10 inches towards a jersey barrier. Pucker Factor: 5/5 do not want.
If you go to a softer spring, try and do a little homework and get a spring that sits taller. You've got a lightish, short wheelbase, Mid Engine/Rear Drive car, sort of designed to 'rotate'. You could also try your hand at doing "DIY" coilovers using your Bilsteins with Ground Control Coilover Sleeves and springs spec'd to a rate and height of your choosing. A lot of semi-budget autocrossers do this...it would allow you to get a somewhat taller spring that was also softer. A lot of cars that are popular for auto-x also have spring perch options that make the perch itself smaller giving you more room for shock travel.