Before Don and his dad could get started on the floors, they discovered that they needed to do some further demolition work. Specifically, they had to remove all of the wiring that had been run through (and I do mean through) the joists in the basement.
I don't honestly know if this is standard practice or not; I don't believe we'll be doing it if we rewire (I think there are little brackets you can buy now to attach wires to other things without drilling through them) although Don, as usual, is the final arbiter of what we're going to do in cases like this (and by "Don", I mean "Don's dad").
In any case, they lost a good part of the morning by having to do this, cutting down on how much floor work they could do, but it wasn't such a great loss, since they wound up getting a massive head start on the electrical work that needed to be done.
For those of you curious about the procedure, they first turned all the electricity off in the house (putting a severe damper on my plans to do my design homework). When you do this, and are working with the breaker box, keep in mind that the main feed into the box is still going to be live. Don't touch it. Next step was to start cutting and pulling. They did this in a mostly-organized fashion, room by room, and followed each line all the way back to the breaker box. Once a breaker was empty, they removed it from the box (sorry, I have no idea how to do this -- maybe Don will comment with his technique, since I was upstairs being cold the whole time [edit: see Don's comment here]).
A large number of breakers were emptied and removed from the box, which is a great start on the rewiring work we need to do. So, not such a loss for the morning.