" What if I stop using Roundup and just overseed the "bad" areas
like crazy with new dwarf fescue, and mow at about 2 and 1/2 inches. I
am
thinking the thick Fescue would eventually choke out the ugly grass --

especially if I mow a little shorter, which the Fescue would tollerate
better than the ugly grass, which is taller. "

That's unlikely to work. You have some kind of coarse, faster growing
grass. A slow growing dwarf fescue isn't likely to be able to drive
that out. I'd take a sample of it to an agricultural extension service
that many states have. If you can identify it, there may be an agent
that can selectively eliminate it. Otherwise, if you have a lot of it,
I'd use Roundup to whack the bad areas all at once, then over seed the
whole lawn. If it really is everywhere, and there is nothing that will
selectively treat it, then you may need to whackthe whole lawn