You already have a funnel. To me your biggest flaw is that your guard station is within the prison itself. If you positioned 2 guards (one necessary and the other as backup) at the funnel behind a door, then in theory you wouldn't need more. But your drawing doesn't make mention of what the clinic is, or really any of the rectangular identifiers.
Your governing process would be more important than the number of guards. You could have 40 guards and run the place badly and it would fail.
If rearranging the prison is possible - you did not say the prison couldn't be expanded or redesigned - you could move the clinic and guard station behind the funnel door, in a transient hallway, leading to an exit funnel that has no way to cross a hellishly deep and wide moat except a draw bridge from the other side.
If the clinics and guard stations had doors to both the main area and the hall, they act like a butterfly catch that prevents them from going through by way of one door not being allowed to be opened until the other is closed. Not beyond 1800 american technology.
Your kitchen is cut off except the service windows in the mess hall within the main room. Kitchen staff cannot interact with guards based on how you designed the food slot system. Use your imagination there, but I was thinking like a McDonald's burger queue. Slide it down a 20 foot pipe and your cooks never see the prisoners. No point of escape there.
All dorms are open so visual check is possible from the guard station across the way. Guards never need to interact with the main room. not even to break up a riot. Your governing system keeps them in check by threatening to lose food privileges or whatever else you want to leverage to keep them relatively sane.
So you have one guard in the guard station at all times. Another guard to accompany a doctor or whoever may need them without the station guard being away from post.
The draw bridge is only lowered by the convoy system that is used both for switching shifts or bringing in new prisoners, which go through the incoming butterfly trap so no prisoners can escape while new ones come in.
If your process was strict, and made sure of a couple things - at least one guard in the guard station at all times, only one door is ever allowed to be open at a time, never enter the main room, etc - you could conceivably run the prison with only 2 guards per shift. 3 shifts minimum. That would not include whatever convoy you have in place for shift management, which would presumably be in control of the elaborate draw bridge handling. But that's really just in the details.
Then you have to consider things like emergency cases where the guards need to flee, evacuation, communications, etc. But that's for another question.