Old Tech,
I have not experienced any problems with the Cross rims or tyres. However for carpet I have used the Tamiya M Grips, kit tyres or S grips. The HPI M tyres work also on the front but have a smaller diameter.
For asphelt the Cross tyres and rims work very well on the rear of the car. I do not use the foam insert, but replace this with a spice 5.5mm insert.
Regards,
Calvin.