Sadly I believe the only way you'll be able to obtain dirt/snow tires using Sony's method is to revert back to 2.11, do it to the cars you want, then re-update back to 2.12.
Off-topic (slightly): Been playing around with the Secret Menu a bit, and have been creating custom races and having a blast (this is on 2.12 by the way, the menu still works!). This really doesn't have much to do with hybriding, but I wasn't sure of where else to put pics like this. If anyone wants to see a few pics of custom races, let me know and I'll post up some pics within the next hour.