Since you have an expansion chamber, just unscrew it from your vertical adapter, and screw in the male Stabilizer.
Use some type of thread sealer for all your connections.
Depending on where your input connector is on the expansion chamber, you may find you need a slightly longer piece of macro line or steel braided line to reach your ASA. The Stabilizer's input is at the top of the regulator. Your expansion chamber's input is probably at the bottom.
Once you get the regulator installed, it will take 2000 or so shots to break in. You do not have to actually shoot 2000 paintballs - you can dry fire it.
To tune the marker with a Stabilizer, remove the air from your marker. Take the barrel off, and look into the chamber at the power tube. Unscrew the velocity adjuster until you see it flush with the INSIDE of the powertube. You don't want to take it out, but you also don't want it protruding into the powertube.
Now get some paint, air up, and slowly increase pressure on the Stabilizer until you're shooting at field speed.
This will give you the most efficient setup using the Stabilizer.