Thank you Michael for great explanations and suggestions!

"Is there any way for you to make it into a solid rather than starting with an open surface like that? That's one thing that may help."

Hmm well...actually the reason I wanted to create the thickness in the first place was because I messed up the form and wanted to recreate that previous state when it was a solid. So I broke it apart and kept the faces that were correct and thought I would be able to puzzle it together somehow.

"Or you might look at some other CAD programs like maybe ViaCAD Pro might potentially have a better surface thickening function than MoI currently has, if you import your model into there that might work."

I did try in OnShape, but it wasn't able to compute either. I'm going to download the demo version of ViaCad and see if it works there.

"The other thing you could do to make progress would be to use Edit > Separate on it to break it apart into individula surfaces, then use Offset or shell on those individual pieces which will succeed and then work on extending planes so they intersected each other, use Construct > Curve > Isect to intersect those planes to get extended boundaries and then build new planes from those boundaries."

Haven't been able to pull this off yet, I'm gonna keep trying though. This seems like a very useful function, I didn't know about it! Thank you for yet another lesson in MoI :)