From my experience, the first 3 numbers on a race tyre are pretty close to the actual tread width of the tyre. The tread with is normally no less than this number and quite often a bit wider than this number.
With a road tyre the first number is the section width - the overall width of the inflated tyre fitted to the correct size rim measured at it's widest point. Consequently a 235 road tyre will usually have a narrower tread than a 235 race tyre.
A 240/640/18 Avon racing radial which has a section width of 267 and a tread width of 244.
A 265/35/18 Avon road tyre has a section width of 271 and a tread width of 235.
A 225/40/18 Avon road tyre has a section width of 230 and a tread width of 203
It seems that across all competition tyre manufactureres, the optimum rim specified is the either the same or wider than the width of the tread, so a racing tyre that suits your rims would be between a 215 and a 225 - i.e. a tread width of approximately 8.5" - 9". Any wider and the tread will 'overhang' the rim width, which could lead to some odd handling when cornering.