rather than go to the expense of new tyres on a hunch, just swap the wheels between the strada and sp, that will tell you if it's tyres. my guess is your steering head bearings are too tight. that, or your fork legs are too far through. a mate has a strada and we swapped for a ride, his forks are through about 20mm (mine are 12mm) and his felt heavier to ride and felt like it was going to tuck in low speed corners. he changed it to 12mm like mine and it feels heaps better.