In case anyone is in need, I just bought this double-sided 2" Velcro on amazon and it works well with the Handy.
It is a much stiffer material than the original strap so it stays locked in place in the slot on the mount, and if you have it aligned and tensioned correctly, it does a pretty good job of staying between the strap ridges on the sleeve (not perfect, but better than the original). Plus, since it is a 10’ roll, you can trim it to whatever length works for you and not worry about replacing it when it needs it.
Note: I’m not an affiliate or anything. Just found something that works for me and, in my opinion, is a better option than buying an original replacement.