When we did ours, we firewalled out everything but our IP that was being used for RDP to the server -- that allowed us to take run the upgrades without user connections. I think there is a "status page" that allows you to see when conversions are complete.
We noticed several things that needed reconfiguring or "initial configuring" after the upgrades as well -
It sounds like you have a much longer process ahead of you -- I almost wonder if setting up a fresh VM, fresh SmarterMail, then attaching the domains and mailboxes from the old server one by one and letting it update them would get you a more "controlled" upgrade process.
I don't know if that would be better or worse. You really may want to go ahead and get a ticket open with them - at least you've got them on the line and primed when you push the button on this --
MailEnable survivor / convert --