Addendum, half an hour later: It's now reached the point where I no longer use that key combination to pull up the "Force Quit Applications" window when necessary. I simply leave it open all the time for quicker feedback and access.
Followup, 2 days later: I whined about this on an Apple support forum and got the following advice from one of their gurus:
[A] Safari/Preferences/Advanced - enable the Develop menu, then go there and Empty Caches. Quit/reopen Safari and test.
[B] Then try Safari/History/Show History and delete all history items. Quit/reopen Safari and test.
[C] You can also try try Safari/Clear History and Web Site Data. The down side is it clears all cookies. Doing this may cause some sites to no longer recognize your computer as one that has visited the web site.
[D] Try un-installing and then re-installing Adobe Flash Player [links provided].
Tried A. Didn't fix the problem.
Tried B. Didn't fix the problem but did succeed in wiping out a lot of my cookies, so I've had to re-sign-in to lots of sites (which fortunately I kept the log-in information for in a separate text file).
Decided to put off trying C and D until I went hunting for the application that kept hanging up on me, namely Safari Flash Player Plugin. Using ⌘-space to activate Spotlight, I tracked the fugitive down to MacHD > Library > Internet Plugins, where I trashed everything that bore the names "Flash" or "Adobe", then emptied the trash for good measure.
Relaunched Safari (for about the 30th time in the last couple of days), and now everything seems to be working fine. I wish I'd tried assassinating the plugin right off the bat.
More followup, later that same day: All was going well until I hit a website that required Adobe Flash Player and offered me a chance to download it. I did so and followed the installation instructions (Version 22.214.171.124 for those keeping score at home). In less than 10 minutes the "Flash Player Not Responding" hangup was back. Well, at least now I know whom to blame.
Final word (I think) on April 25. The advice I got from the Adobe trouble-shooter (after wending my way thru their confusing "Contact Us" procedure), was Please try disabling hardware acceleration. See the instructions in the video troubleshooting guide for details.
Well, I never got around to trying it. While I was waiting for a response from Adobe, someone else had suggested the old standby of shutting down the computer and restarting it, and that seemed to do the trick. Probably something I should have tried right off the bat.
Anyway, all's well that ends well, and I hope this saga-in-installments has provided our readers with some idea of what's likely to work (and what not to bother trying) if the same thing ever befalls them.