There is no heat and air back there.

Additionally, the hardware stores in the area are sold out of pipe insulation and heating tape so I'm not sure what else I would even do if I were close by aside from trying to thaw it with a blow dryer. 

That is indeed considered an "appliance" i.e. 1245 property and eligible for bonus and S179.Oil tank might be part of the HVAC subsystem and thus part of the building if the oil is used for a heating furnace and if the tank is connected to the furnace/building. 

We are happy to keep helping our landlord with this, but running 3 space heaters for long periods of time is adding to our heating bill.

Familiarize yourself with the costs of materials such as types of flooring, water heaters, heat and a/c units, appliances, counter tops, windows etc.

You're lucky you didn't have a boiler & hydronic heat.

However, the market it seems has heated up EVERYWHERE and I need to recover some funds and this project had so much meat on the bone it will give me the ability once sold to payoff my own house. 

Window Kit 112-in x 84-in Clear Heat-control Window Film https://www.lowes.com/pd/3M-Wi...If that doesn’t work, you could try lowering interior humidity (unlikely to make significant difference) or upgrading the windows. 

As for heat, add baseboard heaters.

The house is a 3bd 2.5ba with a ADU with a bonus room (with its own cooling and heating system).