I have resolved the problem with the help of Microsoft Technical Support. It seems that the part of the system which is set up to auto-deactivate consists exclusively of Service Pack I, Beta Edition. The problem may be fixed by uninstalling SP1 with Windows Update, and reinstalling a current retail version of that package. When the uninstall is completed, the OS no longer displays the "Evaluation" watermark. The deinstallation and subsequent reinstallation are, of course, quite time consuming. I started at 12:30 and I'm still working on my second machine at 5:30. But the result is infinitely better than having to wipe the C: drive along with the registry, which was the alternative. I hope that this post will save someone the time necessary to figure this out. It isn't obvious at all that the "Evaluation" advice pertains only to SP1. By the way, I have observed the problem in the 64-bit versions of Win7 Pro and Win7 Ultimate. The processors are quad and hex core i7s, the RAM complement is 12GB-24GB.
Thanks for the help,
Bill