FYI: I'm on a chat with an AT&T rep right now. Seems the issue with ME is that for some reason, the internal AT&T "update database" still has me listed as having my S4, not my S6 ... which is why my phone keeps telling me that no update is available. The rep is correcting that now, and will push the update out to me in just a bit.
(CORRECTION: This issue with my IMEI is effectively resolved, but it may take a couple/few days before I get confirmation on that, and can THEN check for my update)
So, for any of you AT&T people who are showing "no updates available at this time" when you do an OTA check for updates, you MIGHT be having the same problem as me. Would be worth a check using the "live chat" feature on AT&T's website to find out.
UPDATE AGAIN: Talk about good customer service!!! The rep I was live chatting with just called me personally to tell me that he followed the case through, and the database update has been processed, and that as soon as I can get on wifi with a good 4g/4gLTE signal, I should be able to check for the update again and download / install it. He told me that they use the cellular network to ping my phone and confirm the IMEI number prior to allowing the update which is why I have to be somewhere that has a good connection to both wifi and cellular. Unfortunately, my office must be built out of lead, because our cellular signal strength is HORRIBLE in here. Looks like I should be able to get my update this evening at home.
FINAL UPDATE - FOR NOW: Was able to relocate in my office building to a place where I have a good cellular and wifi signal. Tricked the phone using manual time/date function, and was able to download/install the update (YAY!). Just rebooted into recover mode, cleared/wiped the system cache ... and will be monitoring it for a few days to see if I notice any real changes/improvements.