Some months ago I outsourced my mailserver too. So I searched for alternatives which maybe handle mails better than I-MSCP does. Soon I found a software called "mailcow". I find it pretty cool as it comes with a lot of features and possibilites to adjust things like anti spam and co. It also gets regular updates (almost daily). Maybe you should check it out.
To sync old accounts, it has "ImapSync" built in. As I moved I created one sync for each mail account and told it to sync all 20 minutes. So no mail got lost. But there are things like Settings which cannot be transfered (e.g. sieve rules). It also comes with another webmail called SoGo. I personally think it is better but there is a documentation how to add roundcube.
Feel free to contact me for any questions.
https://mailcow.email/ (demo available)
https://sogo.nu/ (demo available)