Let us know what you ultimately choose for your application and maybe include pictures, etc., if it seems appropriate. What you are trying to accomplish is a common HVAC engineering scenario. It is seen a lot in quarantine rooms in hospitals or clean rooms (white rooms) in various industries. It is about changing the relative pressure differential between spaces.
This plan if flexing and changing as I go and read posts here and on other threads. It's changed as I experiment on what works in my house. I'll first describe what I've tried and then I'll tell you what I'll be doing.
What I tried:
1) I tried blowing cold air out of his room and and down the hall towards the stove room with floor fans. This did little to nothing by bringing the temperature up almost 1° over an hour. It was also not practical in our busy house. I tried a combo of fans (one hallway one in his room). And also tried a single fan.
2) the bathroom is at the end of the hall beside his room so I tried using the bathroom exhaust fan and noticed the hallway did warm up slightly by pretty much the same as running the floor fans.
3) I tried running the central air fan and it only made everywhere colder.
What I am currently doing:
I put a small fan on the floor by the halfwall/doorway that leads into the hallway. since the half wall/doorway is where the heat is getting trapped i Angled the fan towards the ceiling so that the air from the floor fan mixes with the hot air trapped between the doorway and the hallway. This floor fan also intersects with the blower of the insert so that mixes as well This alone has dramatically increased the heat transfer into the hallway from 18° to 23°
In the stove room I've been keeping the ceiling fan circulating upwards on medium to high depending on the burn. His room has warmed up from 15° to 19°
What I learned and what my plan is:
In this ranch home it is better to push hot air from the ceiling towards the far rooms and let natural air circulation take place. I think this is because there is only a halfwall/doorway in the way of a straight line from the insert blower fan and the hallway.
I will be using a low profile register/fan combo near the ceiling to move air from the stove room and into the hallway... I will then move air from the hallway and into his room with a short 2 foot flex pipe and a small silent fan.
Natural air circulation should fill his room with warm air and force the cold air out and towards the stove room.
I can could also keep the bathroom fan on to draw air down the hallway.
Let me know your thoughts and ideas for products.