Separate Support Representatives From Regular Users

Currently, anyone who has access to a Client can be assigned a ticket.
I would like to be able to limit the users to whom a ticket can be assigned to a subset of the users who have access to that Client's tickets.
I have a working patch that I will attach, with one minor caveat:
The user performing the assignment will always show up as a choice in the Assigned list, even if they do not have the "support $client tickets" permission. I am not sure how to change that.