I only had a chance to briefly look at it, but I think the problem you had with thickness is due to the small radii (it works if you change the side to thicken). I was going to say offset a surface to the inside and create a inside surface, then cut with surface. But I think if you create this inner surface using a sketch (similar to how you did your original surface), you can knit together an inner volume and then Cut with Surface.
Hope that's clear--again sorry I don't have a lot of time to reply.
I would . . .
- use "thicken" with the "Create solid from enclosed volume" option
- split the solid where your red line is in your PNG
- shell the part you want hollow
- combine the two solids to finish.
Both of your methods work!
I'm still a bit green when it comes to surfaces.