I'd be willing to help you move, if that is your chosen path. What kind of site is it?
rixride makes a valid point about money - it talks. Most limits on email is likely to be anti-spam protection. If you were a host, you wouldn't want your domain getting blocked for
spam, or even the association with spammers. Some communication may be all that you need. Otherwise, find a better host. There are thousands upon thousands of them... and I'll be ready to move you.
Frank