Apart from the import diagnosis which allows in most cases to re-examine the surfaces in volume via "Tried to repair everything", when it doesn't work I convert the file back to STEP once again or to IGES and it allows in some cases to remove the problem.
After that, I don't think there's a miracle solution...
A post with interesting solutions: http://www.lynkoa.com/forum/3d/transformer-surfacique-en-volumique-sw
Even wastewater treatment plants generated in volume sometimes fall back with surfaces following a transformation problem. Of course, if it is created in pure surface, then I think it's dead, unless you rework the surfaces to try to fill or thicken but it can be very difficult or even impossible.
Unfortunately, first of all, simple and surface rarely go together, so when it's also the result of an import, I rough it up to limit the problems and then basta, it's really too time-consuming for the result obtained.
Often it is the threads and tangent faces that are the problem. The former are easy to manage: we delete them. The latter often generate commonalities to several surfaces that are impossible to solve.
This is, in my opinion, SW's downside (I must admit that I don't know the other software on this point): its inability to process step/iges correctly. The sat and parasolid files are indeed less of a hassle.
In the end, my subcontractor sent me the parasolid model and the import went perfectly.
I have tried all your solutions but nothing is 100% effective unfortunately. It's true that trying to solve surface problems is time-consuming as Stefbeno says.