Some of us seem to be on a similar quest. As to what the name Cecchini means I haven't gotten any further than the coin or the snipers.
I live in Curaçao which is part of the Netherlands Antilles. I was born in Holland and my father Luigi was born in Lauro di Sessa Aurunca (Caserta) which is roughly located between Rome and Naples. My grandfathers name is Enrico and his father's name was Luigi. The tree ends with his father Erasmo or Raimo. They all were from this same little village.
I am curious if your roots are also from this region. Any other explanations on the meaning of the name Cecchini are welcome.