One of those empties had the AC/furnace coils, water piping, main electrical panel, and water heater all stolen.

Stick to basics...free standing self cleaning ovens with coil stove elements; refers that do no have through the door water or ice; and if possible (more and more difficult to find) no "digital" touch pads.

My price for a 3 ton, 13 seer system, condenser and evaporator coil, is around $900, add $500 for 80% furnace.

Do buyers prefer free-range stoves over 30 inches Coil Electric Cooktops? 

Courtney, it actually sounds like you need a knowledgeable Roofer that will know how to find the source of the leak, weather it's with the roof membrane or perhaps the A/C coils dripping to the inside (as an example, it happens!). 

The oil burner we replaced was burning a gallon an hour when running and it ran 12 months a year due to domestic coil.

The trick is learning that number.I pay:Interior repaint (3 colors): $1.5 - $2Flooring: $1.5 Roofing: $300 (all in materials and labor no deck repair)Windows: $75 per openingHvac: Condenser/a coil = $3k furnace = 3k (high, but I get priority and zero upcharge ever)All new pex $1500That's a basic list, but you get the idea.

They found the unit had not been cleaned (dirt caked up on coils and the unit was low in freon indicating there is a leak in the system.  

I believe the aversion to electric is coming from the old style stoves with exposed electric coils.

There is a pump in the tub that circulates water through the coils of the heat exchanger.