That is a lovely piece. Spanish dollars or 8 real coins were cut and counterstamped for use in the West Indies. There was no single system in use. References I have create a picture of official marks vying wth chaos and anarchy.
I think the key to identifying exactly where this piece was used is the 'V' shaped symbol. Is it a 'V' containing another letter ( 'T'? ) or is it an arrowhead or something else?
British Commonwealth Coinage
Howard W A Linecar
publisher - Ernest Benn Ltd 1959
has the following possible ( text description only, no images )
Vieque ( or Bieque or Crab Island )
two incuse 'V's one reverse upon the other.
It also mentions that there were unofficial marks, so it could be one of those.
If anyone has more I would be very interested to hear it.