Oh, I can get rid of them easily in the editor - two regex operations take care of things nicely - but that's the thing. I have to manually identify the problem and check for breakage afterward. Details, details...
See, in this particular class of cases, the nesting spans the entire BODY element, and the DIVs have no attached classes. It's literally a matter of stripping out opening DIV tags that come immediately after the opening BODY tag, and doing likewise for the closing ones. Simple and painless, but not universally applicable.