How to add a record to my join table

I completely understand, Mark. Thanks for the assist. Let's just focus on the #1 case. If we solve that, it will be good enough for a while. 

Here is the relationship/field structure in both directions. 
When I view a Patient record, all of this data populates properly. 

However, when I try to add a patient lab by clicking on the "Add Patient Lab" in the Patients table, this is what I get:

Notice that Patient Primary Key is blank, despite this being clicked from the Patient record directly. 

Here is the URL formula for the Add Patient Lab: 
URLRoot() & "db/" & [_DBID_PATIENT_LABS] & "?a=API_GenAddRecordForm&_fid_26=" & URLEncode ([Patients Primary Key])& "&z=" & Rurl()

Also, notice the Lab Primary Key is a read-only field. How do I create a lookup where the user can select from all Possible Labs which one they want? Normally I would think this would be done by a record picker, but it's almost like the URL for adding a Patient Lab isn't populating properly. 
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Solace Sonder
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