OK, so either the fate or my incompetence intervened in a really positive sort of way.
I called to check on my reservation and it hadn't gone through correctly due to some glitch. I took the opportunity to request a differet hotel and got booked into Park Inn. Just spent the night there: while I have no idea what "DFW Airport Hotel" would have been like, Park Inn was just fine, actually quite pleasant. (In case they have different locations, mine was close to DFW and right next to Embassy Suites.)
Now off to my gate at DFW!
Thanks to everyone for their input.