Cpanel transfers are allowed, but it generally comes from another Cpanel server. Sounds like your data is not on a Cpanel server from your first email.
The good news is now that SSH is now offered free for all accounts except for a select few:
[Policy change] Jailed SSH access, now free.
Fee free to drop a ticket to support to see what they can do for you, and if there will be any charges.
http://desk.surpasshosting.com