Sorry, but I don't think if another user (that the process owner) own the datadir it could works properly... (including for quota).
I see various solutions
1/ 1 mysqld process per user
You must wrote a init script for each user, a datadir for each user, and a config file.
I sometime use this multi-instance mysql solution.
That's ok if you have only a small number of users.
2/ 1 database per user
Of course, each user must/could not have the "creata database" right.
and then you must set owner/right on datadir/user (with setgid bit and probably some others)
In this case, innodb table will not be taken in account for quota (only MyISAM one)
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