Not all machine guns are Uzis. If they wanted to restrict it from sub guns, they would say that. I have no idea why it has a problem in the Uzi. The Winchester 9mm load you gave is +p. The +p+ load is the NATO loading, which produces the same results with the four inch barrel as Federal.
Winchester 9mm NATO
Note that in a four inch barrel, it is significantly slower than the Ranger +p load you noted. Have you ever looked at load information that mentioned losing x number of feet per second for every inch you shorten the barrel? This is what's happening here. If you put the +p+ load in a longer barrel, the powder will burn for more time and it will exert more pressure on the bullet than the +p load. The +p+ round needs a longer barrel to generate the velocity, but it will develop a higher velocity than the +p load in the longer barrel.
Changing bullet speed involves more than just putting more powder in the case. The study of it is called interior ballictics. Lots of hobbyists are pretty good at exterior ballixtics, which explains what happens after the bullet leaves the barrel. Interior ballistics, what happens in between when the primer fires and the bullet leaves the barrel, is downright arcane.
They use different powders for different applications. The powders burn at different rates. This is controlled by the shape of the powder granules and by adding chemicals to it to slow down the burn. The amount of powder in the case also affects pressure. If you put insufficient powder in a case, it can actually explode when it is fired. All kinds of interesting things can happen, which makes it as much an art as a science.
But I assure that what's happening is that the powder in the +p+, or NATO load, does not have enough time to burn and produce its full speed. if it is fired in a longer barrel, it will produce more speed than the +p fired out of the same barrel.
Here's a
page that shows the burn rates of various gun powder formulations, and explains a few things about them.