Tim- I see you said you had tried spray on adhesives with no luck.
I was involved in the automotive trade (manufacturing) and we used a spray on adhesive made by Tex Abrasives UK Ltd. We used it for attaching headliners, carpets and anti drum rubber sound deadening on engine parts (timing covers and sump pans); it was also used on urethane foam trim backing and vinyls. It was very good stuff!
I recently used some to fix a rubber pad to a backing plate for a Lidl purchased multi tool after it detached after 10 minutes use from new! The can of spray just happened to be one I had liberated about 20 years ago. If it can attach a rubber pad on a vibro tool like a multi tool and not curl, it should do the job!
Preparation is as always the key to success in adhesive use. Clean and degrease with a good quality brake cleaner, and apply after 2 – 3 minutes when the glue becomes tacky.
The can is marked: Tex Auto – Spray Adhesive. Industrial high strength multipurpose aerosol adhesive, Made by Tex Abrasives Ltd,. Viking works, 113 Greenstead Rd, Chichester, Essex – telephone 0206 870336
No guarantees that the phone number is correct or that they are still in business