Freestanding/portable safe home heaters??
I don't believe there are any free-standing unvented propane heaters that are safe to use indoors. Kerosene heaters are kind of smelly, and some would call them a fire hazard (I don't think I'd feel safe with them), but others use them extensively, and they might be cheaper for heating a couple rooms, and turning the thermostat down.
Your propane useage doesn't seem totally out of order for an old house, but yes, it's a lot. We have a newer house (about 2600 sf), and if we heat with furnace alone, we'll burn about 250g of propane in a month.
(However, we heat almost entirely with wood, so our propane usage is about 200g per season.)
Space heating could save some money, but I'm not sure there's any silver bullet here. If the place is big and poorly insulated, it's going to cost a lot to keep warm. Have you talked to the landlord about spending some money on insulation? Probably a long shot, but a good last resort before you consider moving. If you're good tenants, and you're serious about moving, he could be willing to have the attic insulated or something like that to keep you in the house.