Fly rugs that don't pull

[SpottyBumPony]

I need a new fly rug for Dear Horse but I find they always snag on her hair over the quarters and then tug backwards. Shes a cob but not mega chunky, 6'6 normally. I wondered about a cotton rug instead of mesh but I'm not sure.

Any suggestions? I prefer a should gusset

We used to stitch in a satin material liner patch type thing to help prevent rubbing out manes/coatbat the withers, would that help?