Thank you all for your kind suggestions. Though none were effective in my case, I did find another thread on this forum (from a DDG search) that stopped the beeping. I only needed to calibrate my sticks. It can be found here:
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How to calibrate sticks on Mavic Air Controller>
He has lots of screen grabs that helped me, but if you're quicker on the uptake than I, the text-only procedure is:
(1) Power on the remote controller, attach your mobile device, and launch the DJI GO4 app
(2) In the GO4 home screen, tap on the "enter device" option
(3) On the next page, tap on "Enter the Camera View" option.
(4) Once in the camera view, tap on the three dots at the top right corner (bottom left, in my version of the app) to enter the settings.
(4b) Under settings, tap on the remote controller icon,
(4c) Then tap "Remote Controller Calibration".
(5) On the Remote Controller Calibration page, follow the directions on the screen (which tell you to push your sticks "through their entire range of motion" in a complete circle, around the entire perimeter, repeatedly.
I hope this may help anyone with the same problem in the future.
Thanks again for all suggestions.
Tim
UPDATE: It turned out that while I got the beep to shut up while I was in the Calibrate Stticks page, the little "Finish" button, which I believe was supposed to light up when the sticks got all calibrated, never lit up. So when I just backed out of that page, the calibration did not actually take. So when I shut the controller off, and then turned it on again, the beeping started right back up too. I went through this several times, with the same result. At this point, I have to think my controller's trashed. So, unless there's anyone out there who knows where I can get one for less than an arm & leg, my re-entry into drone flying isn't going to happen any time soon.
Thanks again to all of you for the support.
Tim