What query specific counters / metric if any are exposed for monitoring outside of SQL Server itself?
SQL Server does not expose performance counters for any user defined object. 

In fact PerfMon architecture is not a suitable platform for highly dynamical changes. If SQL Server would provide such feature it has to create counters every time a SP created. Think about SP renames, restores etc. 

A couple of suggestions for monitoring problem of yours would be : 


Creating a wrapper stored procedure for Adam Machanic's sp_WhoIsActive to filter out sessions you are not concerned about and apply practices at How to grant permissions for non-dbas section of sp_AskBrent from Brent Ozar to that stored procedure. 
You can log activities to a table using an agent job like every 15 second execute sp_WhoIsActive filter out unwanted records from resultset log them to a table then let GUI generate reports from that table. With a quick search while i'm writing this answer i have come across a blog post from Brent Ozar. I didn't read the whole post but the idea is same.