My ggg grandfather was Israel Heyes.
And although this in itself does not confer me with any real authority; I have spent a great deal of time researching 19th century records. Names tend to stick long after the reasons for them have disappeared. And the etymology of copse depends on whether the place name is norse or Gaelic in origin.
But even the OED states that a shaw may sometimes mean the edge of a copse, and that implies that you both are right.
It's hard to imagine that the "Cross" was ever meant to signify the religious symbol, as there are dozens of censuses from the period that list any junction--whether of neighborhood or road--as Cross.