The on board kept it lit because the motor continued to receive some fuel. With out the onboard the lack of just a little bit of fuel would cause the flame out.
the perry pump and carb would make no difference in that situation as the pump is still passing fuel with air in it.

while testing a new G2300 I noticed exactly the same problem only from a rich condition, it would flame out if to rich, but in that case a OS F (hotter than stock) plug solved the problem, as well as using on board with the stock plug.

I like my G2300 but it does have it's quirks. I tend to agree with the cyclinder head design could use some improvement. I would bet a twin plug head would do wonders for both the low and top end with or without the stock carb.

One other thing, as mentioned in other posts the carb nipple and tank center line need to be extemely close to one another. Even with a perry pump and carb, I have a tank high condition that makes setting up the idle very sensitive. Seems as though this alignment must be followed no matter what. Gravity is the culprit here.

Mike R