File menu > compact.

Does that help?

No, tried that a few times, but same problem.

I seem to have found a temporary workaround... dragging my Inbox messages to the Trash of my "Customer Service" email account/folder. But that's no solution.

Have you checked that the account you are having issues with actually has a trash folder for the mail to go into? Does the folder have a trash can icon beside it's name in the folder pane.

Yes there has been a trash folder for that account all along. You can see that in the screenshot I uploaded in my first post.

Another observation that might be related... Any Inbox messages sent to my Spam or Junk folders also reappear in those folders. Within either of those two folders, if I select-all, delete everything to Trash (message will show up there, delayed by several seconds), then empty the Trash folder, they all reappear back in their respective Spam or Junk folders! It's like anything that's in my Trash folder gets looped back into the folder from which it came. I also notice that if I use Repair Folder on my Spam or Junk folders, after having emptied them, that that immediately causes their previous messages to reappear.

Yet another observation that might be related to this problem... When I delete email message from my "Barry" Inbox on my iPhone, they're still in that Inbox when I go to my computer. Previously, if I deleted emails on my iPhone, they would also be deleted on the computer; they were "synced".

So I found a solution...

I called my web/email hosting company, they found a "zero link" (m.6656) file in the storage folder on the server, and deleted it. I don't know what that file is or how it got created, but their solution worked.