Gas in oil of pony motor on RGN? How is this happening?

They generally do but with new rings the second ring does its job correctly it also act as a compression ring the volume of gas washs down the cylinder so you get minimal smoking just a lot of gas in the crankcase.

 

I know that's what Honda says, and although this is considered a Stationary Engine, it's not in a static environment. If there is fuel in the bowl, it will slosh around during transit and will find its way through the carb and into the cylinder...which then leaks into the crank.
Your procedure of shutting off the fuel and letting it run out of gas is correct for your application

 

Yes, you are correct. It's leaking into the crank when it's shut off while in transit.
Your float works properly if the motor runs fine.
Here's what I believe is happening.
When you close the fuel valve, it doesn't fully shut off. It closes enough that it can't feed a running engine, which is why your motor stalls/runs out of gas in the closed position. Once the motor dies, the gas slowly trickles into the bowl, and fills it. Your float & seat are working properly, so it doesn't leak gas all over when it's shut off, masking the issue.
Now you begin moving the trailer down the road, during the motions of transit gas is sloshing out of the carb and into the cylinder, where it leaks past the rings and into the crank mixing with the oil.
Because the shut off valve fails in a slight trickle, this is a continuous slow process.
Now when you arrive at the destination or take a break, because the float/needle/seat work properly, the fuel stops flowing, again masking the problem.
You've changed the shut off valve so too late now, but here's how this theory would be proved, try starting the motor WITHOUT turning the gas on. If it starts, then the shut off valve is obviously the issue.

 

I’ve seen quite often a float needle won’t seat completely. The engine will run fine, but while it’s sitting will leak and get into the crankcase.
The only possible way for gas to enter the crankcase is through the carburetor or fuel pump (if it has one). Those are the only two places your fuel system is connected to the engine.

 

Why aren’t you letting warranty take care of the problem? Especially now that there is a noise coming from the motor.