Though it says rubber maid i don't believe they are rubber in any way . I would think they are a type of plastic which one i have no idea, and that is critical as plastics are not all created the same. and if your trying to glue the rubber epdm to the plastic rubber made those are two different materials i doubt anything will work al that great will the epdm primer/gue and a double sided take do the job it's possible. It's a dyi project that's going a little too far outside the box maybe.
me i'd go with a liner and i know that will work .. and i bet the rubber is cheaper than a preformed
Will a standard pvc cement work i have no idea i doubt it's a pvc.
Could a solvent like what is used on plexi glass be the answer . can't say there either
Maybe a polyurethane glue i doubt it, those need to be able to soak into the material.
I WOULD TRY THE SOLVENTS. YOU'LL KNOW FAST ENOUGH IF IT IS going to work it will set in a couple minutes.
https://www.amazon.com/Weld-Acrylic...8769e&pd_rd_wg=XeGjO&pd_rd_i=B0149IG548&psc=1
The other option i'd try is something like this stuff but it is not easy to work with if it's a vertical edge