I've tried every combination of "CLEANUP AND OUTPUT" settings that might conceivably prevent munging my HTML, but nothing works. No matter, what, my HTML gets flattened or in some way rewritten, mainly with whitespace being trimmed off that I want to leave in.
I would suspect CKEditor (version 220.127.116.1175) except that when I tell WYSIWYG to "Apply source formatting", CKEditor doesn't prevent that, so it seems that logically this problem is in the WYSIWYG module. "Apply source formatting" simply causes the HTML to be screwed up differently. Some linebreaks are left in place, but spaces at the beginning of the line are left in place.
How can I prevent this, and still use a WYSIWYG editor?