You could calendar the rubber to the polycarb - the rubber is laid out in a sheet and then pressed into the polycarb after activation with xylene. This way you avoid the adhesive altogether. Not knowing how the polycarb has been formed (web, sheet, mesh) it is hard to know if my approach will...
Look for a xylene based, or at least a high xylene content, adhesive for best results. Trick is to wash silicone rubber surface with a bit of xylene to help "activate" it, then apply your xylene based adhesive to high impact poly. Then join. Should be solid. Xylene based, or high...
I have a urethane/polyester/nylon fabric laminate which we sonic weld at the seams, which forms a channel about 5/16" wide and 1/8" thick. Material is elastic and will be in water now and then also in sunlight. Storage temperature of fabric could reach 125 F at times. I need a UV...