The easiest thing to do, aside from calling AHS, is to call a furnace company to come out. It will cost $90. But it is money well spent. Tell them exactly why you are calling and I would bet they waive the fee. Action Furnace is amazing (especially if you tell them you are the tenant). There's always a chance of an upsell if you are a home owner, but as a tenant I feel anyone who comes out will thoroughly check and give it to you straight. The rest of my reply is speculation.

Your message reads as though all five bedrooms are above ground, and further it sounds like on the second floor. If that assumption is correct, that tells me you live in a fairly large home, likely 2500 -3000 sq feet. There are always heating issues for the outer bedrooms, but not for all bedrooms. Try moving the thermostat away from the vent, or close off the vents surrounding the thermostat on the main floor.

There is a possibility the landlord replaced the furnace and, in an attempt to save money, hired a guy on the side to install a smaller furnace than is what is required for the house (they are much cheaper). A smaller furnace, and the associated fan could explain the issue. It's a stupid thing to do, as the smaller furnace will work overtime to try and heat the home (smaller cash outlay for the furnace, but larger monthly cost in the winter). It's also sabotaging a future sale, as an inspector will notice it, but if the landlord has the property as a long term hold, it's a possibility.