Can’t get our heating tune up in the cold

This is the coldest June I have ever experienced… The weather just refuses to turn warm, since the start of September I have been using the heating equipment! I wanted to turn off the equipment in May, get it cleaned and switch over to AC. I suppose the two of us are going to go from Winter to Spring and right to fall. Summer is getting skipped, no need to worry about cooling. I am more concerned about our heating unit though. It has been working so strenuous all year. It has never gotten a split or even cleaned. The gas fireplace I use has a glass plate. I need to remove the glass in order to clean it. The glass is like molten lava when the gas furnace is on… When I turn off the heater, the glass stays sizzling for mornings afterwards. So I should wait to get a heating tune up until it warms up outside. The complication is this is not happening. I could not go a day without heating. I would also freeze at night without the heater… But, I know our air quality has suffered due to the dust in it. I also know the gas furnace is running absolutely inefficiently. There is absolutely a worn, rusted and abused area in the heater. What can I do? I am frosty frosty and need the heater. I can’t get a Heating and A/C contractor willing to work with that level of heat, at this point I suppose I am just going to hope for the gas furnace not to die, and good weather is not coming, so our gas furnace needs to just hang in there.