As threatened, here are the steps I took. Total time start-to-finish was was ~17 hours. Mind you, I started with the skewer nut on the cassette side of wheel, not vice versa, as suggested by Mark B.
Stuff needed: an extra skewer or maybe a nail
0. Shift cassette to smallest cog.
1. Unlock brake.
2. Unscrew skewer nut. Remove it and the spring.
3. Slowly remove skewer from side opposite cassette while inserting extra skewer/nail in hole vacated by retreating original skewer. In this way you keep your derailer hung, although this turned out to foster a completely delusional sense of security. Do something to secure the nail/skewer in place so that it's inserted deeply enough to hold on the derailer hanger, but shallowly enough to permit you to re-install the wheel after the silky smooth process of changing your tire.
4. In the infuriating manner no different than with a standard bike, use 3 to 4 of your hands to disengage chain, pull wheel from dropouts and down between the brake pads. The skewer/nail which held the derailer in place will of course fail at this point and fall out. Recover as best you can. Also remember to forget just exactly how the cog re-engages with the chain.
5. I installed a slime-filled tube and Vredestein Fortezza Tricomp 700x25s.
6. Check rim for burrs, little men with spears, and other foreign objects. Based on no knowledge, adjudge the rim tape to be sound.
7. Apply first bead of new tire, being careful to ignore applicable rotation direction signs and neglecting to align the label with the valve stem hole.
8. Insert slightly inflated tube.
9. Begin to install second bead. At final six inches, bead strength surpasses hand strength. Try repeatedly, invoking the Holy Trinity with blasphemies so withering as to ensure damnation. For good measure, repeatedly invoke the Universal Malevolent Force known in polite circles as He Who Fornicates with She Who Bore You. With one mighty last heave, focus all your strength and shove. If you're as good as I was , you will simultaneously break your thumbnail, pinch flat the tube, and seat the tire. Slime and blood will spill all over your wheel. The red and green ooze will remind you both of Christmas and one of those Advanced Decompo scenes on CSI.
10. Delude self into thinking that --well sh*t-- since it's a slime tube it will self-seal and I'll just leave it in there.
11. Inflate tire and listen for a diminution of the hissing sound coming from the area of the the pinch flat. When the sound persists, and cruel hope first fades, then dies, remove everything, noting how slime now covers a good part of your rim, and do it all over again with a fresh tube, this time refraining from pinch-flatting.
12. Re-install wheel. Spend an hour trying to line up hub, derailer hanger and stays. With one final shove, you run the skewer through. Only then do you remember Mark B's words to install the skewer cassette-side-first so as to avoid the suffering you've just experienced. Having thus remembered, you remove the skewer (at least remembering to install your "support" skewer on the way out) and re-insert it from the correct side. Of course this time, you'll need to remove the support skewer BEFORE inserting the real deal. You will fail and die.
13. Tighten skewer, foolishly expecting that this alone will straighten the derailer, now hanging at an extreme angle to the frame, the grotesque geometry reminiscent of German Expressionism.
14. When this fails, repeat until the sonofabitch slips into position. Don't ask me to describe how that happens. It just did. It is not at all obvious when the derailer hanger has seated properly. It. Just. Isn't.
15. Test your shifting. This can involve subtle adjustments. The first time I tried to apply pedal pressure, nothing moved. I mean nothing. Nada. Niente. A few more tries and it all fell into place.
16. Also, FYI, somewhere in this process I used a sledgehammer. I believe it was when my "backup" skewer got stuck, badly, and I decided to deal with it Like a Man.
So that's the way it was. OK, maybe not 17 hours, but a long bloody (literally) time.