Hi Jack,
It has to do with the data source schema for the first list. In your InfoPath form, go to data and fields and click on the dropdown next to Main and select the "Firm Profiles" data connection. Expand the data fields. Probably it's not showing a repeating structure and therefore you can't copy the values over correctly. Or, someone is using a concat formula. At any rate, what you want to do is doable but it's a bit tricky to get the filtering right and to copy the values correctly. You could use default values or you could insert the items into your new form. The key thing is that the "Checklists" form should not be using a multi-select but rather you should have a repeating table with default value rows equal to the number of items and default values showing them. You'll use a separate column for the checkbox and you can add a default value to that which automatically checks the row if the item in the "Firm Profiles" list is checked.
We can show you how to do this in less than an hour, but it's more involved than a simple forum reply. You can purchase a support pack from Qdabra's web site under support.
Otherwise, spend some more time refactoring the multi-select and post again with more questions. We'll be here for ya.