Thank you all for your help. I got super excited with the thought of a slipping bushing, but sadly, it's still a work in progress. I finally got some time to test another prop over the weekend. Still popping out. It is a 1966 mercury 350, 35hp outboard. The entire engine has been rebuilt, but for lower end only the water pump and impeller were changed. The prop I tested was brand new, purchased from a shop who said "too old, we don't touch em" when asked about gears. Got the cheapest one possible since it was just a test, feel like it was worth the $128 to test before tearing apart the lower unit. I did watch a video on youtube where a guy ground them down. Think that's my plan since the gears seem to be impossible to find.
The worst part is, I tried to buy a brand new outboard. I had $7k set aside for this boat rebuild, and used only about $600 for the entire interior remodel and exterior upgrades since I already had several dozen yards of vinyl and about 8 gallons of top coat from a 46' carver remodel that I never started. I contacted several stores and they all said they either didn't have any 30-40hp outboards, or they would only sell it to me if they installed it, at a roughly estimated $3k extra. I'm sorry, but I have a degree in automotive engineering, have designed and built vehicles that were shown at SEMA, and have built some of the fasted cars and motorcycles on the planet, there's no way I'm going to pay someone $3000 to run a couple cables and a power line. So....in comes this old trouble maker.