I know that's not what you want to hear but that's my, personal, $.02. They're a fire hazard, especially with children around. Even pets. And, there's a CO2 issue too. And having the fuel around just compounds that hazard. Also, they will 'darken', or dirty, your walls and ceiling over time. And that 'stuff' travels throughout the house!
What I CAN say is that your 'idea' will work but you're, essentially, putting a bandaid on a forever 'bleeding wound'. If the heat pump isn't doing the job, consider electric units or Hot Water Heat / baseboard heat, as an alternative. These units are MUCH safer and cleaner. I wouldn't be adverse to these types of units being used in a garage or workshop, but in the house, I have a completely different perspective. TOO many times I hear on the news and read in the newspaper of accidents and carelessness that causes fires. Truely, I'm sorry about saying that. You can still choose to go your original route but, perhaps, others will benefit from my perspective.