Terry: Hoosier makes a 10 inch high speed rated racing tire (except they are 5 inches wide) Also Center-_Line makes a 10 inch racing wheel.
On our Vintage roadracing sidecars we are using 10 inch wheels all around.
If you were to use 13 inch wheels .......there are a lot of racing tires for that size wheel.
Most modern roadracing sidecars run 13 and/or 14 inch wheels (again a wide tire....but run 50lbs in them and you are running on the center only)