How large is "way too big" for the .SQL file? You could always break the export up into pieces by only doing a mysqldump on a few tables at a time. As long as the MySQL client supports UTF-8, you shouldn't have character set/accent issues, so you might want to check on that.
You could also look into the MySQL Administrator program: http://www.mysql.com/products/tools/administrator/
Failing that... write a script that connects to both databases, and then queries from one and inserts into the other.
