I had the same problem. I loosened the four nuts holding the mounting plate in the engine compartment. I had to pry the plate up with a screwdriver because the gasket had it sealed tight. After moving it a little bit I could get a socket on the 13mm nuts holding the brake booster behind the brake pedal. A note on my vehicle is the clip assembly that the slave cylinder hose went into was blocking me from twisting the old master cylinder off. I have a 2011 rubicon. I did take the fender off completely and the driver door to make access much easier. It was worth the work to make the project easier. After replacing the clutch master cylinder my clutch is working fine.

Thank you very much for the post. It was very well written.

 

There is an easier way to remove the master cylinder which I discovered removing mine to go Chev/Chev Auto setup. Remove the arm from the pedal same as OP stated, disconnect the line same way then get a broad flat blade screw driver and tap the tab at the flange base down on the booster side. Tap not beat. This rotates the master cyl anti-clockwise looking from the firewall side. You only need about 5/8" rotation. This also then exposes the clutch electrical interlock which is then easier to unplug. Install (which I am not doing) is the reverse the procedure. REMEMBER to tap the tab at the base of the flange it is attached to otherwise it will bust off. Way easier this method.