I left some bits of scrap rubber sticking overnight to see with different glues.
The vulcanising glue tubes I have are tiny, and it would need as much as a set of four mats cost to stick down the edges of the rubber to the pile carpet.
The vulcanising glue worked, but only where I’d roughed the surface and I guess cleaned off some release agent, so I expect to stick the patch in the hole gluing around the edges with it.
Also superglue is said to work well, and the test patch was OK on the roughed places, but was weaker and again its expensive for how much I would need and working time is a nightmare on something big.
Some old Black Bostik has the right smells and normally sticks to anything, but just peeled off the rubber, so useless.
I have a big tin of Evostik that might do the job, or I might buy a tin of neoprene glue. Not tried those yet.
I needed to identify what the rubber was before committing myself. Apparently, if it melts with heat it is a pvc base and if it burns and stinks of sulphur it is proper rubber, like this one is. I almost think a pvc base might be better in this application with a heel rubbing because the stanley knife cut the 3mm rubber sheet very easily, or maybe not.
I think the pop rivets will be needed, and just use the glue to try and prevent the edges curling or trapping dirt.