Here's my cheap mod:
I have Mopar rubber floor liners and pulled the carpet from the Jeep. This results in floor mats that move all over the place because the anchors that snap into the holes in the mats are attached to the carpet, which is removed.
First, I removed the anchors from the carpet. It's obvious they were not designed to be removed, ever. The anchor is in two pieces, the top part (which you need) has a ridged protrusion that goes through the carpet and then there's a donut that snaps on the bottom side with a series of tangs that snap past the ridges on the top part to hold it together. You don't need the bottom (donut) part so you can get them apart much easier if you don't mind breaking this part.
Once they are removed, you can discard the "donut" parts, and then use a hack saw to cut the protrusion off of the bottom of the upper part of the anchor. I then used a Dremel with a sanding drum to smooth any remnant of the protrusion from the anchor, so the bottom of each one is flat and smooth.
Now go and mark where they need to go. I used rubbing alcohol to clean the floor and then installed each mat to test-fit. With a pencil I marked where the anchor should be, and then removed the mats and made a large crosshair mark so I'd know where to position the anchor.
Now use mounting tape like this:
3M Scotch 1 in. x 1.66 yds. Extreme Mounting Tape-414/DC - The Home Depot
Put a piece of mounting tape on the bottom of each anchor, as big a piece as you can fit without it overhanging, and stick the anchor solidly into the position you marked. If you get this right, then the floor mats will snap right in and stay exactly where they should be.
In my JKU there is some kind of sound-deadening material stuck on the floor that was in the way of where I wanted to put the anchors in the rear, so I had to cut about 1cm off of the edge of each of the rear anchors to make them "D" shaped in the rear so it would clear the ridge created by the material. I would imagine this is far from universal, so you may have to get creative.
End result? No carpet and mats that don't move.