Not happy with ventless heater

My kitchen area is currently heated by a compact, ventless gas heater.

Because the house is nearly 200 years old and lacks conventional ductwork, it’s problematic to heat and cool.

The advantage of the little heater is that it doesn’t take up much space or require any venting capabilities. Despite the small size, it puts out a great deal of heat. With very long winters and temperatures well below zero, the ventless heater carries a very demanding workload. I’m not entirely satisfied with it. It is a single stage heater, which means that it can only operate at full capacity. There is no way to adjust the speed. The heater is either on or off. When the temperature in the kitchen drops below the thermostat setting, the heater kicks on. It then blasts a tremendous amount of very hot air non stop. Once it achieves the desired temperature level, the heater shuts down and blows chilly air to cool itself down. This creates very unpleasant temperature swings. The ventless heater features two separate air filters that need to be constantly cleaned. I make sure to clean them at least once per week. If even a small amount of dust accumulates in the screens of the filters, a red light flashes on the control panel of the heater. When this happens, the heater will no longer shut itself down. It simply runs non stop until I manually shut it off. I’m worried that the system will overheat and create a safety threat. There’s also the issue that the heater causes an oily film on my windows. I have a set of French doors separating my kitchen from the dining room. Each of the two doors features 12 small panes of glass that I frequently need to clean.

a/c set up