>what happens to the matter around a vacuum?

Matter in a vacuum has no forces exerted on it.

>What forces are created by the pressure differential?

Pressure is just Force / Area.

Pressure ( in this example ) is the result of the summation of forces of gases bouncing off of a surface. There is very high pressure at the front of the shell, and very low pressure at the rear of a shell when fired.

>If you found a way to decrease the pressure differential, what would happen to those forces?

You can reduce drag if you change the shape of the shell. If you have more pressure at the rear of the shell the net force on the shell is reduced. You can do this with a boat-tail shell.

>Which one would exert a greater net gain in speed, the equalization of the pressure differential or the ejection of mass to fill said void in this particular scenario?

The gas sent out of the rear of the shell does not act like a rocket. In a bleed gas shell the gas is going nearly the same speed as the shell, and is trapped there for multiple interactions. The trapping of this allows the gas to exert a pressure onto the shell. If your force diagram model has this gas as part of the shell you have a new drag coeffienct, if you model the shell alone then you have this gas exerting a force ( or a pressure over an area ) on to the shell.

Vacuum doesn't exert a force. The gases released do.

You can look at this from a force diagram. Having a vacuum behind the shell just means there isn't gas pushing on the shell. Adding a gas does push on the shell.