That contrived example doesn't work because head or tail experiment outcome is defined as coin landing with that side up. While the coin hasn't yet landed, it m

That contrived example doesn't work because head or tail experiment outcome is defined as coin landing with that side up. While the coin hasn't yet landed, it makes no sense to speak of "landed head facing up = heads" or "landed tail facing up = tails". The space of events in this case are outcomes of coin tosses. We don't care about what happens while the coin is in the air. To determine if the coin is biased you would need to repeat the experiment large number of times and see if you get experimental outcomes that do not agree with the expected values given by law of large numbers. This is not how things are in quantum mechanics though. Uncertainty principle is an intrinsic property of quantum systems. It's not the case that the act of measuring somehow disturbs the system and changes the measured values. It's that values are undetermined at all until they are measured. And even then there is inverse relationship between how precisely you can know momentum of the particle vs its position. The more you know one the less you can know the other.