Trouble is, I keep getting urgent renewal notices from the "old" registrars.
Do these folks not notice that the domain is now being managed somewhere else?
There are two separate databases of information for domain name ownership: the main one, and then the one the registrar uses. It's not at all uncommon for the registar one to not match up with the real one, usually from transfers but sometimes a renewal not being passed on to the main database and sometimes a renewal that you ordered once going to the main one twice...
I think it's a good idea that anytime you do something to update whois data, registration date, registrar in charge, etc., that you verify that the main records are updated correctly too.