Hello Kgturner.
Not sure of the cork mat thickness, but I suspect it is slightly thinner than 1/16" thick. I have a quite lengthy article about the swap-mod on osageaudio's site, the maker-seller of AIVS cleaning products. The article is under the header of "RCM Museum" on the AIVS main page.
I believe I used 1/16" thick Neoprene Sheet, without a Self Adhesive backing, and used DAP Contact Cement. The first time, I bought self adhesive backed sheet from McMaster-Carr, and the surface was slightly bumpy due to poor adhesion.
It wouldn't have been a problem in use, but it didn't look good, and wasn't to my liking, so I got another sheet without the adhesive backing.
Either 1/16", or 3/32" thickness should be fine.
With Contact Cement Adhesive, the mat will then be basically permanently affixed, but IMO, it will be the last Mat you'll ever need.
Do not forget you'll need to punch holes in the Mat for the Spindle, and also the 3 access Holes for the 3 Screws that fasten the Platter to the Arbor. I used a spent .38 caliber case, with its edge sharpened with sandpaper as a makeshift inexpensive punch.
Just in case you ever have a Platter Motor go bad down the road, you will need to remove the Platter to gain access to the Motor's Mounting Plate Screws. Mark