Jon, before sending your gun out, it seems that recoil is making the gun double. See if the screw under the top lever is timed with the gun, the reason I say this is because that screw head is tapered to the angle of the top tang and means that someone has possibly taken it out. If that screw was turned one full revolution it could pull the trigger housing up and make the sear/s closer to the firing plate. (you could take the left lockplate off and see if the sear is very close to the trigger plate) If so back out that screw one full turn. Also look to see if the lock plate connecting screw ( ties both locks) is flush with the right lock, sometimes 1/2 turn can make the HOT not work. Another is the srew under the trigger guard that comes out behind the safety, this screw should be flush also. This screw can also pull the trigger housing up.
If the HOT works fine using snap caps then I would look into at least the first screw under the top lever as the culprit.