Late to the conversation, but two comments:

1. Hankook RS-3s are a super-sticky tire. One could argue the grippiest out there short of an R-comp. Have direct experience with this. Guessing your friend must have some other Hankook model.

2. As profile gets lower, you need a wider rim to accomodate a wider tire. Without looking I suspect a 275 fits a 9" rim in a 40 series tire, but if you go to a 285 or a 35 series (or both) that may be a bridge too far. Just something to keep in mind.

A cheap summer tire that holds up on track, and there aren't many, is the Sumitomo HTRZ III. Not the greatest tire, but I've chunked out a number of other tires on track and those particular Sumis held together. Tread goes quickly, but once they are down near the wear bars you can get a few events out of them with minimal wear. No idea what sizes they come in in 19", but for a cheap tire they'd do well for your intended purpose.