If you are looking at about 7500 watts that is a 40 amp breaker with the 125% factor applied. You'll need two slots to install that breaker. I have no idea what panel you have but I'd bet that tandem breakers are available for it. By doubling up two existing branch circuits you'd have the space available. For what you are doing, I think this would be the way to go versus the non-vented propane heater.
Tandem Breaker Example 
Unfortunately we just added on to the house in the last few years. Added the attached garage then as well and when we did so we already combined some of the breakers with the tandem breakers. I looked in the panel box and there's 2 that could be combine but that would only free up 1 slot. Not sure if 2 circuits could be combined to 1 to free up a second slot or not. I didn't spend that much time looking at it once I realized it was going to be more complex than just adding a breaker.
