Thanks for the replies.
Now that you guys mention it, it does appear to center up (for lack of a better term) nicely when the trigger is pulled. If I cock and pull the trigger with the cylinder open, I can see the hand moves up a little farther at the very end of the trigger travel before it breaks.
I don't know anyone who reloads ".32 Police Ctg" (which from what resources I can find is .32 S&W Long), but I can buy a box of ammo and pull a couple (well, at least 6, probably 12) bullets to do Jim's primer test. If that works, I can shoot the rest of the box....