Well, this is tricky....
Since version upgrades are preserving the data, this is a road you could follow. You could backup all the stuff you have and start upgrade process. I believe you need to upgrade your v3 to some specific level before you can upgrade it to v4.
When you have managed to upgrade your server, you can backup your database and transfer it to your new host. At this point you also need to reconfigure your agent to connect to new server host.
I haven't never done this, but don't see any reason why is wouldn't work. I would recommend to test this procedure on testing environment before touching prod servers.