Yeah, you see those little rocks behind you? Throw your jacket in there w/ the rocks. You live in AZ, right? Get your jacket dirty with some AZ dust. That'll cover up the shine.
Thanks to the tip from a fellow board member, I used 250 grit sandpaper (you could probably use even finer paper if all you want to do is degloss) to lightly degloss and accent the seams/edges.
Be sure your POCKETS ARE EMPTY when you do this, and when you do the front of the jacket where the inside pockets are, hold the jacket so the lining is not tight against the leather, or you'll sand an interior posket marker on the front.