Parts add up. That is why you need to test them before replacing. I have no problem with replacing a spark plug at $3.50-$4.00 if you are unsure. But make sure you have a quality plug. There are a lot of cheap counterfeit plugs on the internet. Buy your plugs at a Brick and Mortar store. You should use a RJ19LM or J19LM Champion. This is what Briggs designs the engine with. They come with different versions of that plug from the Factory, but it is the basic base line plug that will work well. The non resistor (no R prefix) plug will give a little bit stronger spark. For some reason, from the Factory they always use the R. I do not know Briggs thoughts on this. I won't guess.
If you cleaned the carb as you said, the float is at the right position, It does not leak. It should be fine. You do not need a new one. Did you replace the O-ring seal or confirm it is good? They usually last a very long time. The Chinese cheap carbs are a crap shoot. On top of that the bowls rust very easily. I have seen 2 to 3 year old ones with rust in the bowls.
It appears that you set up the thermostat sail correctly from what I can see in the video. If the sail spring is not the original it may be too light. This is a long shot. I am guessing at what else may be your issue.
It seems if you where at 1/2 choke your issue would go away. As slow mo said you should not run long with the shroud off for long. It is not really an accurate test as the cooling/heating of the engine is altered by it being off.