After conducting further research after this post:

I looked into the children of Thomas Carey/Thomas Cary Gould and finally found his daughter Elizabeth. She married Ephraim Shoemake, and they also had a son.

They named him Thomas Cary Shoemake .

There seems to be a pattern developing with the naming of Thomas, as you suggested before, and although it may have been the vicar who wrote it down incorrectly, I find it interesting that it should be spelt Cary, when his mother was a Carey, and this is perhaps further evidence to Thomas Cary Gould being Thomas Carey?