Neil
I had exactly the same problem and solved it by cutting away the plastic bezel- all the way around so there was nothing touching the glass.I used a dremmel hand drill with a saw blade to cut the the plastic.
I filled the gap with silicone rubber bath sealant to hold things in place.
The grim looking bezel was then disguised by supergluing an alluminium frame over the surface (mitred at the corners).
The thin strip of alluminium is available at B& Q - they now sell small quantities of metal for various craft purposes-I think it was about 12mm x 2mm .
I will try and upload a picture at weekend.