Burnt Out,
Good luck! Galileo proved the equivalence of motion in non-accelerating frames of reference in a famous thought-experiment several hundred years ago (search Wikipedia for ‘Galileo's ship’). The fact that the same misconceptions about treadmill walking/running are still held shows that these concepts are probably counter-intuitive for a lot of people.
You are right in trying to come-up with an analogy that is better understood - I think one of the issues is that the belt surface is not perceived as a constant velocity reference, possibly because it is so small and vision tells us we are stationary. My favourite analogies include increasing the belt size to that of large airport moving-walkways or bigger. I’ve also tried asking what would happen if you were running at 10 mph on a treadmill, which was itself on the back of a lorry driving at 10mph; in this case the treadmill belt would be stationary relative to the ground, and you would be running at 10 mph overground. If people understand this to be equivalent to overground running, then they should appreciate that there will be no difference if the lorry moves at a different (constant) speed, or is stationary.
As to the ACTUAL differences between treadmills and overground running (beyond air resistance), in some recent experiments we showed that treadmill belts can decelerate by 10% or more on foot contact – this reduces the effective speed of the treadmill by the same amount, and the fact that the treadmill accelerates to maintain its average speed when the foot is in the air has no bearing on the treadmill user. These decelerations vary greatly from treadmill to treadmill, so my advice is to stick to the same treadmill, and treat the indicated speed as being a rough approximation to outdoor speeds.