To prevent the mat "getting away" / "running off" as you put it, you could put a bit of anti-slip mat underneath it.
I've been using a 100cm x 30cm rectangle from Wilko for a few years, but in the interests of saving carrying its 96g weight I've just bought some HG Anti-Slip Spray which I'm going to apply to the underside of my Multimat Superlite Compact 25S (which incidentally is 340g, compared with the 513g weight of your Klymit Static V).
The Multimat Superlite Compact 25S is only 119cm (3', 10 3/4") long, and 1" thick, which really only makes it suitable for midget humans or dogs, whereas the Klymit Static V is a full length sleeping mat, which is 182.9cm (6') long, and 2.5" thick, so its like comparing chalk to cheese.
The Static V is a bit on the heavy side though and it starts at around £55...It's only saving grace is that it's available in a range of colours, including woodland camo. However, Lidls are currently selling Crivit inflatable sleeping mats. Yes, they are only available in a horrible bright orange colour, but they are very cheap (just £17.99!) and at 494g (without the storage sack) they are reasonably light too. They also come with a 3 year warranty too, so it's definitely worth a punt