The common practice when racing at commercial raceways was to use glass fibre reinforced sticky tape, mainly to support the mounting pins.

 

Lexan bodies are fairly durable, at least more durable than the butyrate bodies that were sold in the mid '60s. Lexan bodies are sometimes sold in different thicknesses, you may be able to find the style that you like in a thicker version.
When I was racing 1/24th commercial raceway cars those could get scrunched up in a crash, I used fiberglass reinforced packing tape on the inside of my bodies for more strength.

 

A coating of Shoe Goo on the underside of the body will also help. If you can't find it locally (hardware stores), Amazon carries it too.

 

Parma used to sell Mylar strips that had adhesive on one side and they would be applied inside the body where the pins or clips would pass. RC cars might have a similar product.

mike

 

You could also get a roll of gaffers tape and try it - it’s fiber duct tape that doesn’t leave a residue when taken off

 

ShoeGoo on the inside but make sure it's been degreased first.

 

Thanks for the info.