Marc, I did try to work with these surfaces some more. Not having much luck with IDD, the surfaces are very problematic.
Your assumptions are correct. I am suggesting making a good inner skin without the holes and recreate the "cups" with new geometry. The problem is trying to close up the hole where the transition is.
Can you request new import features that may be higher quality data? The 4 "panels" of the surface shape simply are not meshing right and I cannot seem to get IDD to solve it so that a reliable offset can be generated.
If you can get a new import file, see if they can provide it without the rounds along the recessed "cups". Even better, can they provide the native surface prior to the trimming of the edges. I am assuming you want to create your edges anyway and extending these for your purposes may be difficult or in the least, limiting.
Typically, industrial design people provide boundary surfaces to designers without features and often extend beyond the edges. This would be a better place to start from.