Edit: you also say, "if I remove the stem and replace it, the hands pop back into the right positions", but in both photos above with the crown & stem in place the hands look out of position, at least to me. Would be a very strange problem if the hands' relative position changed depending on the presence or absence of the stem. The relative position of the hands is dependent on the gear meshing of the hour wheel, the cannon pinion, & the minute wheel. Something would have to be pretty seriously broken for the gear meshing to slip depending on whether or not the crown & stem are present (not to say that it's impossible, just that it's a strange sounding symptom).
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