In our set up we bargained for a retainership fees and got about 80 % of my demand. I also bargained for a small apartment in the premises. There are always, people looking for a job and a place to stay.
Now, If I appoint an additional Anaesthesiologist, I have to pay additional sum for that.
This retainer fees and market value of rental for the Apartment( Part of deal to the person appointed) is sufficient to square it up.
In effect, the whole thing is free to the group and still the job is done. We also make it a deal with the new fellow, that if the night list is heavy, he has to come in action to help the person on call.
In other words, he is being exploited, but the equation has to work.
You are now able to fulfill the hospital need and still without a burden.
Not that it will be right in your setup, but modify and see.