Andy 69,
Welcome to autocross with street tires. I have an old (86-89?) Birkin and have never had a problem not being able to rotate it. The understeer (205/50/15 x 4) is due to modern tires not working with light weight. As already stated, a hard lift or brake should help. Alignment / corner weights ditto. Without being a serious (huge slicks) autocrosser, Mine is almost neutral, rotates easily and is a blast, just not very fast. I have not splurged on AVON ZZS 15", and continue to hear good things about R888R Toyos. Don't know their wear rating. Someone here does... May try them. How old are the tires? If you don't know, they are probably too old.
Rear fenders don't like cones. Below is a photo of mu cone catcher, just on the off side, I don't hit my side. It is removable. I am only disappointed that it has not sliced a cone off, leaving the base in the square.