I am decended from the Goodship family also but so far cannot find the connection between the William you have and my Goodships. I believe there to be one though as according to records the Goodships from Bisley came over with the Huguenouts from France and can be traced from then in London.
The Goodships were also the families who gave the name France Lynch to the village in Bisley where my family lived for generations.
I also have Gardiners in my tree and presume these too would be connected somewhere. The Gardiners were a huge family.
If you have access to Genes reunited please contact me through there and you can view my tree to see if it helps any. I will see what I can dig out for you too, I can only try my best but hopefully something will turn up. I have been puzzled by this connection too and need answers myself
All the best
Karianne