It's a toilet!
Sorry, not terribly informative. I should have taken pictures of the new flange. DH ended up securing not the lock-tite Sioux-Chief but another of theirs. It has a ring fastened to a pipe that inserts inside the drainage pipe but without gaskets to "lock" it. Turns out the hardware store had many of these on their shelves; they just didn't lead me to them when I asked. The delay was unnecessary.
The old flange was rusted thoroughly but set directly into concrete; it couldn't be gotten out. DH used lead taps, which were hard to seat because the concrete was poorly poured with air pockets and harder and easier patches to drill through, apparently. DH was not a happy camper.
I got the toilet installed but not without trouble and exasperation. Though I'd checked the threads were undamaged for the bolt head, on the toilet one became difficult to thread; took me a whole hour fighting with that thing.
Thank you all for all your help! Water seems to be holding and waste a flushing southward. How do plumbers greater than 100 pounds and 5'-2" even accomplish anything at all? I should think only contortionists need apply.