From your description I would first suspect a fuel issue.
A partial blockage somewhere which is letting a small
amount of fuel get into the cylinder but when it is gone
the motor stops running. Probably should start with the
gas cap. Is the vent open? Is the vent hole plugged?
Check for a filter in the gas tank, is the petcock open or
plugged, possible blockage in the fuel line from the tank
to the carburetor, check the filter in the carburetor,
blockage in the carburetor, is the float bowel filling with
fuel, is the mixture screw open far enough. As far as the
connecting rod issue and the motor stopping in a certain
position, this could indicate some binding somewhere.
If you don’t have a fuel issue you would need to provide
a video of what your experiencing before I would offer
an opinion as to what could be going on.
Tubs.
A "Boathouse Repair" is one thats done without having tools or the skills to do it properly.