Dmitri;
my original conclusion, was the same as your conclusion. And after several experiments, the best result I got was to simply connect a 33k Ohm resistor in series. This worked better than adding an aluminum plate or a mouse pad (which tended to be to mushy & give unstable results)
After these experiments you've suggested I'm perplexed that a 27mm & a 35mm piezo that put out 20V & 30V peak to peak (respectively) would not peak out the TMI (set to 1023 HighLevel). And both generate the same midi number of 74. It makes me think there's something limiting the input.
Sincerely.. Alex