Not much selection in 13" tires. Avon has the widest, but as you note, they are big $. On the other hand they do last forever, given the car's light weight.
I run Toyo R888's on the front of my track car (185/60R13) and they were $133. They have decent tread for rain. I ran Toyo R1's on my street Cat for 10K miles with no issues. The new R888R is suposed to be better than the R 888's. As with any track tire, they are all sticky and will toss lots of stuff into the cockpit.
'97 Caterham Super Sprint, 1700 Crossflow-sold
'09 Birkin S3, Duratec-sold
'03 Caterham Zetec track car