Ok, so this gets a little weirder.
Not only can I log in to iTunes and this site with the Apple ID in question, but it also continues to work successfully on the iOS version of the App Store on my iPhone and iPad. But, the real kicker is that when I checked the App Store on my iMac today... I noticed that 2 of the 3 applications that were waiting to be updated had updated themselves on their own as of today and are listed as the most recent entries under "Updates Installed in the Last 30 Days"! I suppose that the App Store does have a background update capability and I'm sure that it worked this way before, but this was unexpected to me in this situation, since I cannot manually authenticate.
Since 2 out of yesterday's 3 app's needing updates did update... I assumed that my authentication problem had somehow resolved itself. So I tried to manually update the 2 apps showing as requiring updates (1 from yesterday's 3, and 1 new one as of today). Nope. I got the same "AMD-Action:authenticate" error as always. In theory, I suppose, I could live with just background update functionality (if I could rely upon it)... but I cannot download & install *new* purchases if I so desire.
Lastly, I tried contacting Apple for support through thegetsupport.apple.com site. Unfortunately, that was of little help, as the responses I received were of the variety: "Although I am happy to assist you in anyway that I can, I am limited on what I can do technically. We have a great team over in our Technical Support Department that will be able to work with you over the phone in order to resolve this issue for you." I thought it was maybe the heading I had selected on the getsupport site, but I tried twice... once under "Account Management | Using an existing Apple ID on Mac App Store"... and another under "Connecting & Downloading | Connecting to Mac App Store". Apparently the getsupport site really doesn't link you to *Technical* support, but rather just customer service representatives that cannot themselves forward your case to the proper Technical support teams. Very disappointing. I suppose I am going to have spend all afternoon on the phone to try and contact the right person.