After moving mail server to separate (virtual) machine and applying same configuration as on first Postfix+Dovecot and friends server, all went smooth without any downtime thanks to Dovecot replication.
The problem has arisen a bit later when it turned out that Gmail does not import e-mails from accounts configured es external ones, ie "Check mail from other accounts" feature.
Operations from existing accounts and creating new ones resulted in cryptic message:
Server returned error: "Connection timed out: There may be a problem with the settings you added. Please contact your other email provider to verify the correct server name and port."
However receiving with mail client were working fine. After crawling interned for hours and tweaking with configuration, double checking everything, still no-go!
It turned out, that the issue was with the IP6 connectivity. Removing IP AAAA DNS entry for mail server resolved issue.
Well, untill IP6 connectivity will be fixed. If You have similar issue try checking IP6 connectivity, as it seems that Gmail only tries IP6 connection if available, and does not fall back to IP4.