Basically have many huge delimited files that I know I can import as a table, but I need to map that data to an existing rational multi-table MySQL database. There should not be
I'd suggest using the ETL(extract translate load) tool from the Pentaho Business Intelligence package. It's got a bit of a learning curve but it'll do exactly what you're looking for. Their ETL tool is called Kettle and it's extremely powerful once you get the hang of it.
There are two versions of Pentaho, an enterprise version that has a free trial, and a free community version. The community version is more than capable but you might give the enterprise version a test ride too.
Here's some links
Pentaho Community Edition Site
Kettle Site
Pentaho Enterprise Site
Update: Multiple table outputs
One of the key steps in your transformation is going to be a combination lookup-update. This step checks a given table to see if a record from your data-stream exists and inserts a new record if it does not. Regardless of whether it's a new or old record it's going to append the key field from that record into your data-stream. As you keep going you'll use these keys as foreign keys as you import data into related tables.