I've got a server with a database that's about 10G. I need several
other copies of this database, with different names, on the same host
and same MySQL instance.

I could mysqldump the db and then restore it into the others...

mysql> create database one;
mysql> create database two;
...

mysqldump ... > dumpfile.sql
mysql -uroot -p one < dumpfile.sql
mysql -uroot -p two < dumpfile.sql
...

Unfortunately, each restore from a mysqldump takes about an hour (and
if I do more than one at a time, they'd slow down considerable due to
disk I/O contention).

If these DBs were all MyISAM, I could shut down MySQL and just copy
the directories. But it seems that InnoDB tables are stored partly
in /var/lib/mysql/ibdata1 and this database has a mix of MyISAM and
InnoDB.

Is there a better technique to make several database copies quickly,
that works for a mix of MyISAM and InnoDB?
-- Cos