----" absolutely beautiful condition "------But it appears to be a " pig with lipstick " in reality.-----Cut the floor out and fix it or take it to landfill.
Do a compression test till gauge stops moving up.----Or pull bypass covers to look at pistons rings.-----A 60 year old motor often needs a complete teardown in my opinion.
Find some " prussian blue " AKA " mechanics blue" and check tooth contact.-----Change shims as needed to get correct tooth contact.----Needs to be done or gearcase might come to a " dynamic halt " in the future.
On some of these ( I can't see the parts ) the prop thrust washer can be used to turn the bearing carrier.----Left hand thread.-----These lower units are not robust.----I recommend you take it apart for inspection / reseal with a complete kit.
I can not see your parts !----Some did use 2 keepers.------Does your motor have the original lower unit ?----One piece lower shift rod ?-----Any pictures?
Take starter apart !-----Inspect test it.----Take ohm reading on armature.----If bad you have the smoking gun.----Guess work on outboards often does NOT work and gets expensive.