I start by making a few assumptions:
- Your geometry is not too prominent.
- It can get distorted quite a bit.
If these are true, you can use this trick.
There is one possible way. First you start by baking the height of the flat geometry. There are a number of ways to do this, see here for some possibilities:
How to make a displacement map from existing 3d geometry
Armed with the height map you model the Möbius strip. Unwrap it (hint: you only get one side). Then add a displacement modifier to it (you probably also want a "Subdivision Surface* below. Level four or five should do it.). Set the Displace to use the height map. Also set it to UV (messed this up myself a few times) and decrease it's strength. You can finish with the combo solidify-edge split-subsurf lv.2. For optimum results set the shading to smooth.
I hope this helps.