Just a thought, When the boat slowed down, was the shaking you described accompanied by the motor trying to rev to higher RPM’s like it went into neutral? When it revs high, the rev limiter starts cutting out one cylinder which will make it "shake and chunk" like crazy until the RPM comes down by reducing throttle. If so, I’d bet the prop is slipping on it’s thin rubber shock absorbing mount to it’s hub. The fix is to replace the prop. Taking it off, you won’t be able to slip it by hand. You can mark the prop’s position on its hub, put it back on, let it shake/fail again and then see if the prop moved on the mark you made. It’s unlikely it will stop at the same place on the hub. There used to be shops that could replace this rubber hub to prop interface, but I haven’t heard of one for decades. You can get a new prop reasonable at http://www.propcopropellers.com/.
Dave

You so need guidance from a knowledgeable LOCAL club member. Many members know (and love) these classic Johnson engines and have years of experience. They will look the motor over and watch it run. Then they will help for the pleasure of getting you and you engine running. No profit motive. This is a great hobby. When starting we all have a learning curve then it gets easier. Get with a member.

Looks to me like California, so that leaves me out. It would be a long service call from Cape Cod.

I guess I missed previous posts, so what hp is it, please?

When an engine stops abruptly in forward, the prop and lower unit are noting but drag; so the motor will pop out of the water, if not locked down. Being in reverse probably has nothing to do with it. Does the motor restart right away and run smoothly at low speed, right away? If it won’t crank over right away, it may have over heated and seized up.

If it’s free to turn over as soon as it stops, and its a 35 hp, I like Dave’s theory about the rev limiter and slipping prop….