Replacing props underwater. Lesson learned?

That remains to be seen. Riding the keyway is still a possibility. Putting the key upside down with the wrong radius in the bottom of the keyway is another possibility. Removal of the broken shaft in the propeller will help complete the story.

If the shaft is a 3.5" diameter AQ22, the installed Safety Factor is 3.51. Or another way to look at it, for a recommended Safety Factor of 5.0 (minimum for highly loaded recreational diesel installations), the Shaft Diameter for AQ 22 would be 3.932", round up to 4.0". The AQ 22 Torsional Strength for shafts from 3" to 12" Diameter is only 36,600 psi.

If the shaft is a 3.5" diameter AQ22 High Strength, the installed Safety Factor is 6.72 or for a recommended Safety Factor of 5.0, the Shaft Diameter for AQ22 HS would be 3.168", round up to 3.250". The AQ22 High Strength Torsional Strength for shafts from 2-1/4" to 8" diameter is a more robust 70,000 psi.

If you do not have AQ22 High Strength Shaft Material, you have a design/engineering problem as well!

Good news from a design / engineering perspective. It is a conservative approach and well within industry norms. As a side note, the corresponding recommended spacing between bearings / supports would be 119" for 3.5 diameter AQ 22 HS Shaft.

A standard SAE Propeller Hub Length would be 3 x the Shaft Diameter, in this case 3 x 3.5 = 10.5" Long. A look at Propeller Diameter would yield a max of 15 x shaft diameter, 15 x 3.5 = 52.5". A more conservative approach would only allow for 13 x shaft diameter, 13 x 3.5 = 45.5".

From OP's first post...........

"Needless to say the other shaft is going to get inspected and the prop resinstalled when we haul out in Miami. "

Have not only the other shaft mangafluxed, have both pieces of the broken one done as well. It will "enlighten" all of us, (pun intended) . Its cheap, simple, quick and very telling when looking for stress cracks

If you don't mind, do you have the following:

Full Load Displacement?
Full Load Speed?
Pitch?
Brand / Style of Propeller?

That is a nice turn of speed for that size of boat and power.

Based on the information, the Cavitation Potential rates in the Medium range. Somewhat normal for a production boat.

I personally would have gone with a 2.25 or 2.5 / 1 gear ratio to reduce the tip speed a bit and still keep a 3.5" AQ 22 HS Shaft, but that is "Monday Morning Quarterbacking" for you. At least you know it is not a design problem, would check the Port Shaft thoroughly as well.