In the meantime though, I had picked up something slightly more expensive than a cheap DVD player at Sam's Club: a new DVR / DVD recorder combo. This unit has a built-in QAM tuner, so it can tune all of the local HD broadcasts on the cable. And although it only records SD video, it will record a 16 by 9 broadcast and redisplay it. This turns out to look remarkably good when upscaled by the TV and certainly better than the horrible picture we've been getting on analog cable channel 2 locally. So it's a nice upgrade that looks to remain useful in the future and was relatively cheap. It's going downstairs on the family room TV.
The DVR upstairs has been instructed to henceforth record "My Friends, Tigger and Pooh" each morning. This will make Katie (and daisy_knotwise by extension) very happy.