To start, your Yokohama tires have a different rubber compound than say a summer rubber. The sidewalls tend to be softer and the rubber on the tread tends to be harder. Notice your tires seem to come off in chunks while the Bridgestone's I had on the front of my car looked like they were melting away. That said allseason tires even in "slick" form won't give you the glued to the road feel of summer tires because of the compound itself. It will take more time for the tire to work on the track as it takes longer for it to warm up.
If you look at new tires summer or all seasons they look to have the same amount of tread but yet treadwear on the tires are far less for the summer rubber (aprox 200-220) and even less for "R" Compounds (40-60) and all seasons (280+). Softer the compound the faster the tires scrub off but better the adhesion so there is always a trade off. Also don't forget about the space required to store everything! In an ideal autocrosser world we would all have a set or "R" Compounds for the track, a hydralic jack, a set of street rubber and store our cars in the winter
Forums:
Best thing to do is check the forums and also talk with as many people as you can regarding used rubber/rims. You might get lucky and find a REALLY good deal on rims/rubber, best to always check the forums and jump on the opportunity when it comes available.