Beginner Question: Trouble turning a field with comma separated values into a multi-valued field
I think your best bet would be to use a many to many relationship. Generally this is done with a table for the records (like you have now), a table for the comma delimited field and a primary key field with rows for each of the entries (one for x, one for y and one for z) and a third table with nothing but that keys from the other 2 tables.

So, in your join table, you might have a section of 3 rows with the same key on the main table but different entries for the reference table.  This link explains it reasonably well.