I had a similar problem with the exhaust melting the indicator! Fixed it with an exhaust extension that you can see here:
I agree with Paulc re the aluminium backing plate. Our number plates in NZ are aluminium with a plastic coating. The white plastic coating on my bike's plate is only slightly discoloured at the edge from the exhaust. The bike burns a little oil, and I suspect it's the oil rather than heat causing the discolouration. Make your backing plate a few mm larger than the number plate and put washers between to make an air gap and you should be good.
Stimpy just lookin your tyres , continental trail atac , any good ?
Africa Twin , BMW R1100RT, 2 Bikes twice is happy