It is well known that large amounts of power can be utilized from the floor into your punch, however what method is best/generates the most power into a target for a right cross/gyaku zuki? Heel down or heel up? Some people say it depends for example if you are getting charged at then heel down is preferred for stability etc, but say the target is more or less stationary in front of you (person, heavy bag) which method do you believe would create the most power/impact/damage to the target, back heel on the floor or off, and why

I can't see any reason to keep the heel on the floor in regards to making the punch more effective. If getting charged at maybe, but even then it is probably still best to lift the heel especially if you move out of his way first Keeping the heel down restricts forward momentum and follow through (power) as well as speed, reach and agility.

What about better stability on impact, transferring shock from the ground through your body/arm into the target, kime. Keeping your back foot on the floor doesn't mean that you have less push off power as many people argue, in fact you can learn to use a push off and sinking motion while planting your foot to the floor for power which makes a much stronger base and kime effect to better transfer 'shock' deeper into the target rather than follow through which you could loose position/balance (especially if you miss). Keeping the back foot flat stops over committing to the strike but maintains power where rapid follow up strikes from the legs or arms can follow from a sturdy good position. (remember boxers dont need to worry about getting thrown/took down!) However i do lift the heel now and again for certain strikes but for the main in a self defence (not a sport) situation i would highly recommend the karate planted back foot/heel method imo