You are right, blocking one of the holes sounds great, “in theory”… Honestly, I have never tried it. I thought the pop rivet might be an option, but it surely could loosen up/come apart with all the vibration of a running engine. The other thing to consider is just what kind of restriction having something in one of those holes might cause when the choke was in the open position, while running at high speeds…Could cause running issues. I suppose this could be tried as an experiment, if the engine was yours and you could monitor it, but releasing it to a customer is a risk.
You could try loosening the screws “just slightly”, not enough to pull the peened threads through the shaft. Once loose, you could pull the choke shutter down towards the bottom of the carb throat so it will be a better fit. Once the bottom of the shutter is pulled down, this will allow the choke shaft to rotate more in the closed position which might seal it up at the top of the throat. But again, this is an “experiment” on a customer’s engine.
I will bring my 8hp carb to Rocky Hill if you want to try it out…D