Greg's insight sounds true:
"Your matt is sliding across the floor, I assume in the "downhill" direction…
If you essentially "bond" your matt to the floor, the floor will transfer that to the corners and sidewalls, pulling them downhill with you. . . . That might not be a good thing."
But in practice, if you're sleeping on a slope steep enough for this to be a concern you're not going to get any sleep anyway. Mats will slide around on silnylon without any slope, just from tossing and turning.
The Velcro idea merits a try. I'll buy a pint of Michigan craft beer for the first person to post pictures and a report on such an experiment.
Of course anyone claiming the beer has to show up in Norton Shores MI to claim it. Offer good for one year. Offer void where prohibited, etc., etc.