Joe, thanks very much for this detailed reply. I've just read it twice, and will do my best to pursue your suggestions. Much appreciated.
It occurred to me after sending my first note that perhaps the TD-1K's brain is actually reading the continued vibration of the cymbal pad. When the cymbal is suddenly made to stop vibrating, this then is interpreted as a choke and the appropriate sound is introduced. I don't know how it would do that. Perhaps some internal weebble-wobble thing whose resonance is read by a magnet and thus converted to an electric signal.
But the pad does seem to have a specific area which you should grab, thus suggesting that that area is a real MIDI trigger in its own right.
In any case, Logic / Drum Kit Designer, I'm guessing, simply reads the velocity of the hit and generates an appropriate volume and decay. I.e., it doesn't matter if the pad is still vibrating or not; it's only the initial contact that's processed. (I'm guessing.) We then tell Logic to choke whatever that decay is with the appropriate MIDI message, EO, FO, as you say. So, as you're saying, we're hoping that a MIDI signal is indeed generated by grabbing the pad. If we find that, then we try to re-route it / re-assign it to the appropriate choke notes (E0, F0) in Drum Kit Designer.
Maybe that's just repeating what you said. Sending it in case it's possibly helpful for anyone else reading.
Really do appreciate your fast and detailed feedback.