If you had to update your dns nameservers with the new vps which most likely you did have to do because shared and vps would most certainly be on another sever. Then with that in mind has your dns nameservers fully propogated and updated? If not it might not recognize your licenses on the new account until this happens. If you are using ip based address until it updates this could happen as well.

You might also consider checking your header.inc.php's dolphin and ray for proper paths and periodic see more files if they changed your cpanel login/account name at all.

I've moved from several hosts including vps before with no problems. I did have to wait a little for the propogation.

Regarding the rms, you can still have a shared hosting type of account and then use a 3rd party rms service such as cyberxing for only $1-$3 per month, and you don't have to worry about installing and configuring rms on your own server.