The Iso Offset Node creates geometry that doesn't deform well through Subdivision. Therefore, I am looking for a way to force it to maintain a quad topology, or a different method to make it retain its shape during subdivision.

You'll not get Quads out of it. It's doing a bricker thing to it.

So if you have to come through the iosOffset you're going to have problems. Do you need to subdivide? Perhaps you could increase the sampling of the isoOffset.

If you do need to subdivide try the tri divide sop, as its name suggests it is designed to do subdividing on tri polys.

I've recently been mucking around with resampling meshes, a good way is to scatter points on the original mesh, then copy metaballs to it. You can also use a Particle Fluid Surface which gave me some clean results. The problem is then that you have a “bag” that follows the original topology, it can be difficult to delete the side you don't want.

Try the iso offset sop, much better for that kind of thing and no internal walls to worry about.