Got an Elgin 12s that had a very loose hour hand. Kept hanging up on the second hand or the minute hand. You could lift it off the pinion with a pair of tweezers.
Tightened up the hour hand and now neither the hour or minute hands move.
The watch sets easily with a little friction. I don't think the canon pinion is loose.

What's my next step?

You tightened the hour hand so much that it is locking the hour wheel to the cannon pinion. That completely locks the minute-intermediate-hour wheel mechanism. Pull off the hour hand and polish it out until it is a (very) light press fit

Thanks Dave,
Exactly the info I was looking for. I knew the symptoms didn't point to a loose canon pinion.

Finally got it! There's a fine line between hands too tight and too loose!