Migrating to IRedMail advise needed

Hi to All,
I'm new here. Trying to migrate an old mail (plain text + mysql) server to IRedMail (ldap). By migrate I do not mean moving the old users accounts and maildirs, although if someone has some advise in that, it would be also welcome, but I do not think it is worth it since the old authentication system is postfix by plain text and dovecot by mysql etc. quite horrible :-)
The new server sends mail just fine. I have problems with receiving mail though. What I would like to achieve temporarily is to have both servers oldmail and newmail receive the mails so that I could smoothly add new users to new server and start adding the current users to the new server.  I tried to change the DNS records (5 newserver 10 oldserver) but the effect was that if the olduser is not present on the new server the mail returns to sender.
The advise I would like to get from someone is either how to make both of the servers recieve the mail simultanously or other ideas how to move smoothly from old to new server, considering there are few thousand users which as I mentioned above it is rather not possible to import to the old users to new server due to the fact of different password hashing and different paths and lack of ldap.
Any help appreciated :-)
best regards
PiotrAF