Congratulations and good luck! Man, I know just how you feel, starting this adventure! If it helps any, our land loan was at 7.5% and it didn't kill us, though we paid it off in short order (~4 years). We had the slightly better interest rate, but you are starting out with a house, not an old trailer and a need to build a house like us- that's a great situation!
When do you hope to move?
You said no heat. We moved into our (long-unoccupied aside from a squatter) trailer on this property with no heat, so I know whereof you speak. You're about to know where all the pipes are, so you'll know the heating priorities to keep them from freezing. :-)
Let me suggest a window unit heat pump as a relatively cheap stopgap/ possible longer-term solution. We wouldn't have done that as a permanent solution for a standard house, but we did okay for four years in that trailer and they work fine in our new house since it's earth sheltered. For 1200sqft, you'd need two, plus some tolerance of variation in temps between rooms, but one would keep the pipes from bursting if placed properly.
You're in the South, right? A heat pump isn't a great source up north. But since you mentioned drainage problems, you don't want unvented propane heat (another common Deep South solution). Those propane heaters vent out water vapor. If you have drainage issue on top of that, you're likely to get moldy walls this winter.
Here's one of the options at the site where we got our most recent pump (methheads stole one for the metal after we moved out of the trailer, so this was about a year ago).
http://www.totalhomesupply.com/Window-Air-Conditioner-Heat-Pump-p/amana-ah093e35axaa.htmIf you go this route, compare and be sure you're getting a heat pump with backup electric heat strip (for when it's too cold for the pump to work well) rather than only heat strip (much less efficient for temps above freezing). You will likely have to install/ have installed a 220 circuit and appropriate electrical receptacle to use these. Some big window AC units use the same power setup, but not all.
Another, possibly better option is a mini split system. They cost more, but not as much as installing a big heat pump and ductwork, and they'll cost less to run than a traditional furnace. If you want to refinance with a traditional bank, they might be more acceptable, too, but talking to bank people is the best way to find out about that. Check with local credit unions if there are any, by the way. They are likely to be more flexible in general, not just about heat.
Just do something before the first hard freeze since you'll have the pipes all fixed up by then!