You got me going with this one, I took mine apart. The safety does exactly as I suspected, it has no other function than to lift the hammer off the sear in the cocked position. In the hammer down position it serves a similar function, it blocks the hammer from moving back, but only after passing the half cock notch. So, you need to take yours apart as there is no good reason that the safety will not engage with the hammer down. The fact that there is room to move the hammer back enough to pass the half cock notch means that it should easily be engagable with the hammer down UNLESS something is holding the hammer back behind the half cock notch. I was again impressed with the design of this pistol, I assumed the safety also blocked the sear or sear bar, but it is totally separated from it. You need to take the grips off, then carefully turn the safety down while holding your finger over the detent hole on the left side as the detent will fly out if you don't. Then slide a shim of aluminum under the safety on the right side at the back, it's just to keep from marring the frame as you pry it away with a screwdriver. You will see that there is a specific rotation where the RH safety (Ambi side) can be pried off to the right. Then the left side can be slid out.
I went a lot farther than that as I wanted to see how the disconnector and sear worked. The ejector is held in place on the left side of the hammer by the hammer pin, as is the disconnector on the right side of the hammer. If you don't take the hammer pin out the safety should go together again easily.
Thanks for the question!