Modeling MultiLayer Insulation (MLI)

If you have one layer modeled (as a quilt) try using a transform of the surface rather than an offset. This is available with paste special functionality (move copy) or flexible modeling move using constraints. If you use a linear translation along a line you may be able to get a representation that works for you.

Your offsets are probably failing due to radii becoming degenerate. The move translation should avoid that problem.

This is the gold stuff on spacecraft? Here's how I'd do it:

1. Save your assembly as a shrinkwrap. Use "Faceted Solid", lowest quality setting. This will give you a rough polygonal cover of your model.
2. Open the shrinkwrap and remove the Solidify feature, leaving a quilt.
3. Offset the quilt. Set the option to "Automatic Fit". This should take care of any intersecting surfaces. It won't create an accurate offset, but that's not really an issue here.
4. Use Warp to take care of any detail work.
5. You could try an Auto-round to smooth out the sharp edges, but I had limited success with this in my test.
6. Maybe thicken, if you want it as a solid? Use Automatic Fit here as well, if it won't solidify on Normal to Surface.

Or, if you have access to Freestyle, that's probably the perfect tool for this job. Start with a sphere and just mess with it until you're satisfied. You can even crinkle it easily if you want to.