Materials:
1" slip ball valve
Barrel (I used CPVC)
Tools:
Drill
Dremel
Plumber's Goop
Oral Syringe
Electrical Tape
First off, take your ball valve and rotate the opening roughly 45 degrees. The opening aligns with the handle, so line up your drill with that and drill a 3/8" hole.

This should be large enough to wiggle a dremel in there to open it up just a bit more. If you really wanted, you could just drill a 1/2" hole to start, I could not so I used a dremel to get me there. Make sure to keep the hole centered vertically and at least large enough for your darts to fit through.
Now, either drill through the center of the valve or flip the breech over to repeat this process on the opposite side. This time, make sure the hole is large enough for your barrel to fit through.

Next, use your dremel to grind out a channel down this side. It does not need to be perfectly straight, but it must be wider than your barrel, as it will need to swing through to function.

Wrap electrical tape around your barrel to fit the inside of the ball valve. Leave a small gap (maybe 1/4") between the tape and the end of your barrel, as this is where your adhesive will go. Place the barrel and tape inside the ball valve, so that the end nearest the tape is not sticking out of the ball. This is a good time to test and make sure everything can rotate and the holes line up with the barrel, as gluing comes next.

Using the oral syringe, apply Plumber's goop around the end of the barrel inside the valve. It is important that you not use too much, otherwise it can seal the ball to the PVC case.

Let it all cure for a day or two, then you have a functioning hinge breech. The good thing about it is that it is easy to operate, easy to make, and easy to afford. Unfortunately, it does not lend itself well to any sort of clip system, and it is easier to do with a larger size ball valve, which means your blaster's air output needs to be larger than the typical 1/2" to accommodate it.