Caged Inflatable

I'm trying to make an inflatable that is inside a tetrahedron-like cage, such that the pressure of the inflating mesh makes a kind of bubble around the breps that define the cage. Ive tried it with brep collision, and it seems to work for a few seconds, but I think once the pressure gets too great and the inflatable surface goes on the outside of the cage brep, it doesnt register anymore. I've made the surface normals into longer lines to diagnose if there is any collision happening, which there seems to be initially, but then after 2-3 seconds it doesnt work anymore.

I've kind of gotten it to work, but I think the problem might be that I need a very large number of subdivisions on the inflatable to register enough detail, and even then, as some point the inflatable passes through the brep boundary...

The file has a very small portion of a much larger project...

Any suggestions?