I'm hoping someone can help me with this --

I have an upstairs bedroom measuring about 300 SQ ft with only one floor mounted duct. Duct volume is quite low, and there seems to be no return in the room. The room has double doors opening to a hallway, opposite the wall where the floor duct is located.

When the doors are left partially or full open, the room temps pretty well match the rest of the floor, but when the doors are closed, the room gets quite hot in summer and cool in winter. I assume this is due to the fact that there is no return and that the there is very low air volume from the one duct in that room. There is a good 3/4" of clearance from the bottom of the door to the floor.

I was wondering if simply cutting a 30 x 8 hole in the wall (next to the doors to the hallway) and installing a return air grill on both sides would give me enough negative pressure to get the temperatures closer to the rest of the floor, or do I need to install an air exchanger? Volume in the ducts are low on the entire top floor, but the other two rooms and hallway seem to be just fine. Installing a heat pump to cover the top floor would be ideal, but I already have 3 in the home and do not wish to incur another expense such as that. What would be my best options here? I have had a few HVAC contractors in to look at some of the issues, but they weren't much help...

The home is about 6400 SQ ft including the basement, ground and top floor. There is an air exchanger - but only for the bathrooms. The main heat pump is a 5-ton, with a minisplit and the garage and another minisplit for one office on the ground floor. Aside from that one room, there are no other real heating / cooling issues.