This should fix the issue in most cases, but the ideal solution would be fixing the issue in Quadriflow instead of doing this.
I can try to look into this again on the quadriflow side if you guys want. I might be able to solve that the verts are sometimes moving off the border edges, but I can't promise anything.
It might be working looking into this for a few hours, but if it's more than that I would just go with the workaround.
Maybe it's possible somehow tag bisected vertices and preserve that information through quadriflow remeshing, rather than relying on the vertex positions.