I believe the reseller version of Cpanel ( WHM? ) is capable of moving accounts to other remote Cpanel servers with ease. Sadly I know little more than this.
Perhaps you should request that your current host makes the move for you, of course you may not want them to know you're intending on moving before you've safely backed up and etc.
You could also check the CPanel documentation.
Probably not all that helpful, but a *bump* none the less
Good luck!