Seems like the pedestrian counter-flow (left side) method would work fine if there's not too much traffic so you don't encounter pedestrians on both sides simultaneously or if there's room (and a custom) for the pedestrians to temporarily step off the path. But with higher traffic density I could see an issue where you have pedestrians coming toward you and no where for either you or the pedestrians to avoid each other and therefore both having to come to a complete stop until the pedestrians or cyclists on the other side move out of the way.
At least when everyone stays to the right there's always the option for the cyclist (or runner) to temporarily slow down to the pedestrian speed while waiting for a passing opportunity. In practice I find that I can almost always make slight adjustments to my speed so as to time my passing of slower MUP traffic for a moment when there's no oncoming traffic. I think that would be harder on a heavily used trail with pedestrian counter-flow.