Just a few questions:
1. Do you get alot of water in firebox?
2.( From the pix I can't tell) Where the continious pipe exits the terra cotta is flat or rounded or cracked? The chimney cap.
3. Have you tried the run a water hose to see if the chimney itself is leaking? Not on the top but the part that meets the shingles by the flashing.
My chimney cap is concrete/mortar and it slopes to make like a bubble. I have also heard it referred to as a "wash". Is there to keep water from going done the terra cotta. If you get alot of water going down the inside of the pipe into the firebox. It could be that the cap is not big enough. My pipe exits terra cotta and is 6" ID, my cap is like 10-12" wide and low profile to keep water from dripping into the pipe.
I would try hosing the roof near the flashing not the chimney cap to see what is up. Maybe have wife/child do it and you inspect? If no leak there it might be the wash/top plate? I know you may be uncomfortable and if so, I would not reccomend it but I would have to see for myself! If I was closer I would gladly do it for you.
It seems that your installer has done all they are capable of. I would have to know for myself what was done and if I can make it better! If you do go up with ladder, strap it! Also don't lean it on the broad side of the chimney. Lean it on the narrow side. If the chimney is weak it is possible to push it over! Not sayng it is but can't tll from pix.
BE SAFE
