Autocross/Road Course driving on 15" wheels. What's your experience?

On most cars, higher pressure on fronts and less on the rear.
Even for rallycross its recommended to air up rather than down - that's partly to make sure the tire stay on the rim.
I think running unequal size tires makes it more difficult to get the 'balance'.

If you have or can borrow an extra set of rims, end of seasons used to be a good time of year to pick up used race tires. I assume it still is.
Even better if you have a friend close enough swap or borrow a set already mounted.
@CPDave brought an old set to a T&T and we ran them back to back against what I brought.
That's how I ended switching from the Street TDs to the RA1s.
The difference in precision and feedback outweighed (pun intended) the fun of being able to hang in well past the best grip point.

One thing to be aware of with race tires and near race tires is the optimal cambers they want. Whatever you look at when you got to spend the big bucks on new, check the manufacturer's recommendation. Another thing is operating tempoeratures. A lot of the 200 TW near race tires (labeled street but really sold for competition in the 200 TW classes) are not recommended for use when temperatures are below 50*F. Based on your location - that could be an issue. There are r-comps that can be used down to 32 (although not ideal of course) which means they are more versitle than those particular ultra-high performance summer tires.