Do you have ssh access? you could do the following:
login to ssh
tar -cvf yourusername/backup.tar /yourusername/
bzip2 -9 backup.tar
(enter new username)
(enter new password)
(wait around for a while while it transfers)
wait until you see "226 File successfully transferred"
ssh newhost.com -l newusername
bzip2 -d backup.tar.bz2
tar -xf backup.tar
mv * ..
(complete steps to backup your databases using mysqldump)
You could probably even hire www.websitemovers.com
to move all your data to the new host.