Hi ME
I used Chiropody padding for one of my refurb jobs. You can buy this on ebay, and it comes in various thicknesses up to 10mm thick. I have not seen this in any of our local chemists – hence suggesting ebay.
It is available in sheet form. One downside, but it may be an upside for your application, it has adhesive on one side. But maybe two 5mm pieces stuck back to back would work for your application.
Search for Hapla felt.
Best regards Alan