My problem was fixed. Here's some details.
I contacted Apple for help and they were immediately available and very helpful. The first person I talked to admitted that the account was showing other issues on his end and he was not sure how to correct it so he bumped it up to the next level. The second person quickly saw some bigger issues and suggested that "engineering" get involved. I was told that there should be a resolution in a day or two.
Not waiting for an email I contacted the second level guy two days later. He wanted to make sure that the iCloud account was set up and enabled (I had disabled it) in Mail on the computer. He asked me to select Mail > Mailbox > Erase Deleted Items in the iCloud account. I wasn't sure why I was doing this since the Trash was empty and storage was still showing 4.5GB for Mail, but I did as I was instructed.
After I did that I checked the storage again and it showed 3.8GB! A few minutes later it had dropped to 618KB!
I asked what they did and he indicated that apparently their servers did not pick up my request to delete soooo many emails at one time. I had selected almost all of the email to delete all at the same time.
Whether there's more to it than that I'm not sure, and I don't care. I do know that before I called them there was a problem and after I called them there is no longer a problem. The key to all of this might be the Bold part above, though.
I will say they were very quick to assign someone to me (within a minute), and very accommodating, and quick to resolve the problem.
I think the original problem stemmed from trying to delete such a huge amount of email at one time. I don't think I will do that again.