If you don't have a weight or checkball under the pump shooter then normal heat can bubble fuel out of a carb in great shape. The checkball is to stop that.
There is no way you can avoid trapped air in a heater core with both outlets on same end. It will have to have an internal divider to work that way or the coolant would simply short circuit from inlet to outlet and no heat at all. The internal divider means one pass must possibly trap air regardless of how you hook up hoses.
Ford has been making double sized hose end hoses for forty years trying to force people to buy more factory hoses. A quick trip to parts store for a plastic reducer or even better Home Depot for plumbing parts to make a metal reducer that lasts forever. Been doing it to use bulk hose (MUCH cheaper!) for the same forty years. On my stupid Focus cars with 9 pieces of hose, all I use is the main upper and lower radiator ones, the other seven are replaced by bulk hose using the reducers. I checked the Motorcraft official parts prices as compared to bulk hose and $102 dollar savings on hoses alone! When the metal tubes finally decomposed into pieces on my Mustang II 2.3 I made up copper ones for little or nothing, they lasted the life of the car. Hint, I rebuilt the engine three times, car had like 450,000 miles on it, and one very tired Mustang II when it was all done.
Who cares whether the outlets are all the same size, they do it to make you cave in and spend more money. Not this boy.......