UPDATE: I managed to fix the kick, I share what I did in case anyone finds it useful.

After cleaning up all the mess made by the wrecked foams, I re-soldered the piezo wires to the jack plug: the red wire to the end of the resistor, the black wire to ground (i.e. the top terminal with metal)
To replace the foams, I bought a car sponge, cut it up and reshaped it into two sponges, one for the beater and a smaller one to hold the piezo and make it touch the head.
Finally, I've used hot glue for the piezo to the sponge and the sponges to the metal plate.
The solution works, but the cuts are not precise and this led to unwanted retriggering. So I've had to refine the settings in ext. trig by lowering the retrigger value and increasing the threshold. It's still not perfect, as I get retriggers occasionally, but overall it's playable and the fix only cost about 3-4 euros for the sponge.
Cheers
