you are correct, assuming what you call the inlet jet i am calling the needle. the tab on the float suspends the needle and opens or closes the fuel inlet or "seat" as the bowl fills.
have you removed the rubber plugs to uncover the pilot jet and removed it for cleaning as well? usually soaking the carb with the pilot installed isnt sufficient. also, pay attention to the plug orientation, there are 2 per carb and it makes a difference where they are placed.
nothing wrong with priming the cylinders, saves alot of rope pulling. best to use pre-mixed fuel to be on the safe side. same fuel for your chainsaw, weed eater, leaf blower, etc., if its fresh.
just built a phazer for my youngest. he enjoyed it over the christmas holiday.