Plus there's the problems of storing the fuel and liquid oxygen.
I would think these are compartmentalized (you don't want to store the oxygen with the explosive fuel), and I agree that opposing exhausts would probably interfere since the path from the burning fuel to the exhaust is straightforward for obvious reasons.
AFAIK most (proposed and built) back-pack type units used the pilot's body for control - swing your legs about to change CoG line.
Hmm, this is a good point. A back-pack type device may be an easy way to go, and i could probably test my hypothetical machine in a room with a tall ceiling, or even outside with my legs tied to a rope. Simplicity is key.
So, I have come up with this contraption to that should maintain stability. Imagine you have a long pipe. At one end of this pipe you stick a propeller so that its blades are perpendicular to the length of the pipe (like a helicopter). At the other end you tie a counterweight. Now, pretend that there is a high powered motor in the pipe and so the thing flies.
I would think that it wouldn't tip over and here is why - if you remove the propeller and you hold the pipe, its basically like holding a well balanced hammer. You can do this at home.
The easiest way to hold this thing is with the counterweight at the bottom. If you try to rotate (ie like tipping the heli) it to place the counterweight above your arm, it will be difficult since each extra degree of rotation will increase the sine and increase the required force to tilt it further. Hence, the most energetically stable geometry would be with the counterweight at the bottom and the propeller exerting force upward.
This would be fun to play with using some kind of conventional motor and propeller - it should be fairly easy to balance a flying object! However, I do not know how much thrust conventional motors could generate and if this would be enough to lift the motor itself. If it is however, feel free to experiment and use the above mentioned balancing - ballast , keeping in mind that the trade off here is weight vs thrust. The ballast removes the need for sophisticated steering gadgetry at the expense of being heavy. Your call.
