I usually wear longer gaiters but they're so heavy, been thinking about making something smaller, you have now stimulated ideas
Maybe you don't need the loop that goes under the foot. Let gravity hold it down in place. If you were walking through snow the gaiter would rise up, but you're just trying to keep dirt out so maybe there's no force pushing the gaiter up. The loop will get chewed up by rocks, as in your picture, but it's easy to replace so I guess that doesn't matter.
Maybe they'de stay in place if the elastic made the gaiter just slightly constrict against your ankle. Like have the gaiter form a sleeve and run a piece of elastic inside it. Maybe have a closure so you could adjust length of elastic.
Since your ankle is at it's thinest right where the top of gaiter is it won't tend to ride up.
If the fabric had enough stiffness it wouldn't collapse and the top go down.