The amount of air you can blow through the exhaust back into the engine will be highly dependent on the position of the piston.

You say the engine is unstable, but don't give a better description. More info is needed to better assist you.

Will the engine idle? If not, how long does it take to quit? Will it idle with the glow charger attached?
Can you get the engine to peak RPM? If so, what prop are you using, and how fast is it turning? A tach will help if you have access to one.

Does it transition from idle to full throttle smoothly, or does it cough and sputter before it picks up?

Better information will lead to better answers.

An air leak doesn't always mean a poor running engine. A large airleak from the back plate or fuel intake lines will keep the engine from developing a good vacuum, which will prevent good fuel draw.

As for the time to shutdown, that may just be a mis adjusted throttle stop screw or a minor adjustment to the carb linkage.

Brad