What is the damage to the grey plastic part?
I bought some of this mirror film for a different project, but I had some off cuts. I decided that I thought it would look good if I covered the grey plastic side on my base unit (this was the side tha was showing into the room when the base was in use) and I thought the grey a bit dull.
The plastic was smooth and in good condition. I cut the mirror to fit and trimmed with a craft knife. When the mirror finish was in place it looks excellent. If your panel is still fairly smooth but maybe badly discoloured this may work for you. If your pannel is warped this will show badly in the mirror. The base you stick the mirror on needs to be smooth as imperfections will show up.
I have a cut off about A4 size I can post if you think you might be able to use it to repair.
Stoobie
PS I have tried to include pictures so hope they are included when I prees to post this reply. The pics are not very clear but give you the idea