I'm leaning towards using a joined table, but there are some things you can do to make the "manual" part of it seem as if you are doing it all in one spot.
While in the same breath giving you the reporting and insights to your data.
Have you experimented with an "editable" child table on the main submissions form? This would be your joined table, but you basically be a grid edit child list. Makes it really easy to add multiple records at once.
Your app set up would look something like this:
Submissions --> (have many) Product Assignment
Product Catalog --> Product Assignments
Then you can create many child records from the Submission form, while using a drop-down from your catalog table.
Give you the same affect as a multi-select table without the hassle of maintaining the list.
