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Edit: You could remove just one (1) 3/8" hex head bolt from the brass shift connector in back of the plate halfway down the long exhaust housing... if the shift handle still doesn't move, then yeah, that shaft is frozen. Just be sure to get that bolt reinstalled exactly where it belongs so as not to shorten or lengthen the shift rod measurement.
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Without actually being there, it would be "guess" work for me... however, you did say that the gearcase lube is in essence normal, so I would assume that there is no rust, corrosion, whatever in the lower unit that could jam any component.
The horizontal shift shaft under the powerhead is the most likely area to jam and I've encountered that many times. If, when you attempt to shift, that shaft doesn't move at all... not even a 1/64"... yeah, that would be my "guess".
There is a grease fitting there, should be anyway, but it's too late for that now if the shaft is jammed. Heat from a hand held "propane" torch has always been my first choice... BUT... if that doesn't free it pretty quickly, and although it's time consuming, the best route is to bite the bullet as the saying goes and remove the powerhead to do the job right.
If the shaft is damaged, get back to me as I may have a few left in my remaining stock.