Oh, yeah, I did install those! That's what got me from the "This page cannot load" screen to the Windows Update error. It was late, and I forgot to mention that.
But, it's all moot now, as somehow I managed to get it to work!
Apparently I was almost there. I needed only to install a couple of cumulative IE6 updates (I forget the KB numbers; the laptop I had the VM on died this morning, so I have to wait until I've copied everything off its drive to check what they were), and then everything just worked! A .NET update (1.1 SP1) complained and wouldn't install at first, but I retried it and it installed fine the second time.
Now I have to find the post-EOL updates and install those!
c