Tim, I did know you already did the valve thing but could not say. Wanted to stay in good with Jerry. He is having a bad hair day.
Jerry, and now I, want to know the answer to his question. When it runs a minute and dies, does it start up again with no squirt? Does it start up again with a little squirt?
This is a "start up again" question NOT a keep it running question.
I fear an electric pump. They put out too much pressure. You have done what Jerry suggested I.E. loosened valves. Can you see a way to do my suggestion and take carb apart? Check it all? learn about it? Play with it? see all the parts are there per the video? Report any findings? Don't need a kit for that if careful with gaskets. Just leave them attached to whatever piece they stick to. You took the top off several times, you were already almost there. Nice clean bench, nice clean cookie sheet or cardboard box lid, good lighting, camera........ easy as pie. piece of cake. If it was me I could not wait to inspect it and find the fault. Where is your science discovery spirit? This little, simple, carb is an interesting little gadget. I get the feeling the carb was sitting in your garage a long time. In Missouri. It could have "corroded". Condensed inside, formed scale/zincosis and blocked passages. Mildew. Mud Dobbers, Etc. Rubber on the needle "took a set".