I've used a number of different carpets over the years and it seems to me that the result is always the same - no matter how rugged or robust it is, they break down on the back side. The glue which holds the carpet pile together goes all powdery from saltwater and is a total pain in the *ss to sweep up. I've tried gluing on sheet rubber (as well as those rolls of 'perforated' foam material that we use for dinnerware and such) for non-slip to the back side, but it eventually gives way as the carpet breaks down. I use 3M Spray77 glue. Applied to both surfaces before sticking them together. And don't be shy on how much you use. The limiting factor will be the carpet, rather than the glue.
That said - I don't really see a better option. We need carpet in the PNW, and regardless, I don't think the plain white sole looks at all appealing.
I typically use Home Depot carpet now, rather than more pricey stuff and still get about 5 years out of it.
The PO on my boat screwed down snaps for his carpeting along the edges, and I have always thought to try them out. They certainly look like they'd work!