I am still concerned as to why/how exim would restart. It shouldn't. I've never seen it restart. I have a DirectAdmin powred CentOS6 system running but not hosting any accounts. I stopped exim on it a few weeks ago and it has not restarted.
Perhaps some function (adding/removing a user/domain/account) is causing it to restart when it shouldn't.
As far as moving accounts without losing data:
I don't like suspending accounts on the o9ld server to move them to a new server; it can cause a lot of downtime if the move includes a lot of sites. I've also occasionally had backup/restore problems on suspended accounts. But some sites will need to be suspended. If so, I suspend the entire user, mainly because individual site suspension in DirectAdmin is relatively new and I'm not sure if all bugs have been worked out of it yet.
We let users know before moving accounts, as far in advance as possible. We give them a time-frame during which they should NOT attempt to change static account data.
Identify (as your users) all accounts which have visitor-modiable content (blogs, forums, etc.), and those only you'll probably need to suspend or have users either suspend the site or it's modirfication features during the account move.
Then in this order, at the appointed time/date:
1) change DNS TTL on all zones to 600 (ten minutes)
1) move accounts, but not point DNS to new server as of yet.
2) suspend sites identified above as needing suspension, on both servers.
3) move DNS to new server.
4) Move (again) but only databases and email to new server.
5) Unsuspend sites on new server as necessary
5) Six to 12 hours later again move email only to new server to catch any unmoved email delivered to the old server because of sending server queue/cache issues.
Note this is a work in progress, defined over the past few days because we're moving all our clients to a new hosting latform over the next six weeks. It may need some refining, and your input is welcome.
Thanks.
Jeff