Optimizing speed in mesh collision simulation

I'm working on a mesh relaxation simulation where I'm sort of "thermoforming" a mesh grid over various objects to find a relaxed, draped shape.  My issue is that the mesh is falling completely through some of the objects I'm draping over.  I suspect that it has to do with the fact the the collision part of the simulation is looking at the nodes of the mesh which are colliding with other mesh objects, and my mesh is probably too coarse, so the nodes are sort of being stretched around these small objects/faces and this makes it seem like they are being ignored completely.  When I refine the mesh the whole problem becomes too cumbersome for my machine to handle.  

More specifics:

I'm laying this mesh over convex hulls (which are closed meshes) of 3D digitized points and lines, so these objects I'm draping over sometimes have very small, or very long and narrow faces, and sometimes these objects are very small themselves.

Does anyone know of an alternative way to build the draping simulation such that the program is looking for face-face collisions as opposed to point-face collisions?  Or is there another approach I can take here that I'm missing?  I'd like to be able to use a more refined mesh than I am currently, but the simulation seems to get too bogged down when I refine too much.