SDShooter:
If I release the trigger immediately after the hammer releases, it will only fall to the safe position. If I delay releasing the trigger slightly, the hammer will stop at a "half-cocked" position. From this position, the gun will fire, and if the hammer is pulled back slightly and released, it will fall to the 'safe' position.
THERE ARE NO HALF-COCK OR SAFETY NOTCHES ON A S&W HAMMER!!!
You need to better understand how your double-action revolver works before you go any further.
A little lever, called a "sear" is mounted in the front face of the hammer. The trigger has a little lip or ledge that can push on the bottom of this lever and as the trigger is pulled in the double-action mode the ledge rotates upward and forward. Since it is pushing on the bottom of the sear, it causes the hammer to rotate backwards, until the ledge rotates out of contact with the sear, and the hammer falls and fires the cartridge in the chamber in front of it.
With the hammer in the forward position, you release the trigger and the ledge on the trigger now rotates downward and forward. As it does so it depresses the sear, and it is pushed back into the hammer. When the ledge has gone far enough so that it is below the sear, the sear pops out to its original position because there is a spring behind it. Because the sear pivots having the ledge catch the hammer while you lower the hammer is not a certain thing, and the sear was never intended to be, or to be used for, some kind of a safety while lowering the hammer.
Unfortunately what works with other handguns, such as 1911 platform pistols or certain Single Action revolvers does not do the same in most hand-ejector/double-action revolvers, and this observation includes but in not limited to Colt, Smith & Wesson, Ruger and Taurus.
When you pull the trigger all of the way back and hold it, ALL OF THE SAFETY DEVICES THAT PREVENT AN UNINTENTIONAL DISCHARGE ARE DISCONECTED, AND THEY DO NOT BECOME FULLY FUNCTIONAL UNTIL THE RELEASED TRIGGER IS ALL OF THE WAY FORWARD!
I strongly recommend that any revolver that has less then a full sized cocking spur on the hammer be modified to double-action only (DAO). Otherwise do not cock the hammer while the cylinder is loaded. If you must cock a revolver with a bobbed hammer spur, point the muzzle in a safe direction, AND EXPECT THE POSSIBILITY OF AN UNINTENTIONAL DISCHARGE!!!