Acrobat DC can't send from non-primary group

I have configured each of my Adobe Sign users with two groups as follows:

1 - "Company" - Primary - not able to send

2 - "Department" - able to send

All users have the "Company" group as their primary, and this group is not shared. The "Department" groups are shared with themselves. The goal is for users to be able to receive and sign personal private documents (e.g. HR docs), and these documents will remain private as they will be associated with the primary, non-shared "Company" group. Documents that users send for signature can only be sent from their shared "Department" group, so these documents are visible to the rest of their team.

The problem is that with sending disabled on the primary group, it is not possible to send documents from Acrobat DC, but only through the Adobe Sign website. Attempting to send from Acrobat results in a "You are not authorized to send documents for signature" error.

Has anyone else encountered this situation and come up with a workaround or better approach?