what you could do it login into mysql itself and export the databases.
at a command prompt type in :-
mysqldump --opt --all-databses -rbigdump.sql
it will put all your databases into 1 sql file named at the end of the line feel free to change this, however I wouldn't remove the --opt as if you do it loads the dump into memory and then outputs it, this could be a problem for large databases.
Any problems post back here and will see what I can do.