Don’t know about the polymer additive doing ya any good here, the stuff is tacky but as far as being an adhesive for sheet goods I don’t think so.
I’d wager a non water soluble carpet or sheet vinyl adhesive would be adequate and have a much higher chance of success for your application. Here’s one for just over $40 from typing in carpet adhesive into the HD search bar.
https://www.homedepot.com/p/Roberts-...95-4/202261817