Cloth sewing + subdivision?

Subdividing a mesh doesn’t combine well with the edges you set up for sewing. Is there a way to fix that? I want more vertices for the cloth sim but I still want to keep a relatively simple base mesh.

Depicted is an extreme example, I took a cube, beveled it and deleted the faces of the bevel. The result is sewing lines that stitch the cube’s faces back together. The back row is doing that with an un-subdivided cube and applying sub-d, then cloth physics. The physics are set up with pressure 1.5 and sewing to illustrate the issue.

The front row is a cube that was manually subdivided before doing the bevel thing.

As you can see the automatic subdivision only has sewing edges between the un-subdivided vertices and the sewing lines are subdivided, making them less effective. The manual subdivide is what I’d like to get, un-subdivided edges between the vertices of the faces, stitching better and not leaving gaps.

Is there any set of modifiers or plugins or whatever that could do this? I’d rather not force a lot of extra vertices into my base meshes, that makes them annoying to work with.

Reorder your modifiers?

Then I’d have too few vertices for the physics.