jmc:
WOWIE! Thanks to your suggestions I got it to work! What I did was 2 things:
(1) Repair/Remove duplicate triangles
(2) Mesh/Separate connected surfaces
After that, slicing produced this, which looks 100% correct:
Many thanks for getting me on the right track. I've been going round & round with this for a while now. And in fact the situation is even more complex than this because I want to include the underlying surface on which the ribs are built. And, there are 2 of these surfaces - an inside and an outside. So that will be my next step - adding the underlying surfaces.
FYI the first thing I tried was just step (2) above. That produced a list of 32 items in the Models window. I wasn't sure what I was supposed to do with these, so I just sliced the whole thing. It was noticeably better - the missing diamond shapes where the ribs overlap were not missing - but there were still missing pieces and parts of layers at the bottom, where the ribs join the bottom piece.
So on a whim I added step (1) above and that did the trick. Apparently the combination of both is what has to happen to do a complete cleanup of duplicate triangles.
I also tried Mesh/Mesh Reduction with a couple of different values, but this did not work well. One time the part came back looking like little bites had been taken out of the ribs, and another time S3d simply crashed and disappeared. I have used Meshlab to do "quadric decimation" before with pretty good success, so I know the overall concept is good. I reckon the key is properly specifying S3d's Mesh Reduction/Length Scale parameter . I'll try fussing with that.
Thanks again for all your help with this. I've got several different versions of this part I want to print, so I'll be busy for a while now.