Thanks for the response, Will.
The way the flow works, when a Lead is considered an MQL, it is sent over to SFDC where a Lead assignment rule kicks it into a queue. The BDR reps then takes ownership of each record as they have time to follow up.
The challenge occurs when, while in the queue, a direct inquiry action takes place, elevating the MQL to an SAL, which means the record should be converted to a Contact and assigned to a Sales rep. So it's not that I need a Contact to be owned by a queue, it's that I need to convert a Lead to a Contact that is currently owned by that queue.