Finally, I stopped spinning my wheels as myself, and installed the beast logged in as Administrator.
You wouldn't think you're not the administrator of your own computer, but you're not.
Why this computer forced the issue is beyond me. I installed the free versions of these things before as myself.
You can't use reason, however, with an unreasonable PC; it's either the PC's way, or the highway. So finally, hands clasped in prayer, the Nth installation finished without a hitch, thanks to Administrator, whoever you are.
Windows XP doesn't make it very obvious either, how to log in as Administrator, but that's a subject for another blog.
Having learned this other lesson already, I made sure to tell the installer to leave Report Service configuration to me, and made sure it did NOT try to steal port 80.