Captain Gadget . . . . .
I had exactly the same problem almost two years ago to the day: ISP/AOL, separate e-mail host for domain name, plus port related e-mail problems. After much aggravation and research, moved to Port 587 and things worked perfectly until I changed ISP some time later.
Things may have changed in the intervening period (re: ports), but I'm sceptical about recipients not seeing your specific domain name, as opposed to AOL's. I had no problem; the rider being that I'm assuming you are using your e-mail host's POP3/SMTP settings, rather than AOL's.
But surely the whole thing could be tested in the space of about 90 seconds, but resetting Port 587 in the 'Properties' of your preferred e-mail client (can always change back) and then sending yourself a test e-mail?
At least you would be able to see if it went, came and more to the point who it was from (!).