the burnt hair for the heating component

I am going insane trying to remove the burnt hair smell from our air quality. I am in a rental house & since day 1 it has smelled care about burnt hair when the gas furnace is on. For AC, the house has no smell. Once I change the thermostat over to heating, the hair smell comes back. If the gas furnace turns off & then back on, back comes the stinky smell. I have done everything I can believe of to remove the issue. I upgraded the air filter a hundred times trying to improve the smell. I vacuumed the inside of the Heating, Ventilation, & A/C system. I even stuck a clean brush in the air duct to do our own air duct cleaning. I am now thinking I need an media air purification system or to get a real Heating, Ventilation, & A/C business to do the task. The hair & dirt must be deep in the Heating, Ventilation, & A/C or the air duct. A real Heating, Ventilation, & A/C specialist with enjoyable tools could handle the task. What are the options that our property owner will Springtime for something care about this? I am not thinking likely since our Heating, Ventilation, & A/C does work well, it is just smelly. That is why I might go the air purification route instead. An media air purification system is not all that costly. They are made for removing odors from the house. But, odors care about food, garbage & smoke are fixed by air purification systems. Can an media air purification system repair a burnt hair smell that the Heating, Ventilation, & A/C creates? I honestly hope so since I am desperate. Candles, incense & cleaning the house doesn’t do anything.

electric heater