Hi rjb1984,
I have a Thomas Bundy chr 5 jan 1662/3, bur 11 Apr 1735, married to Elizabeth, possibly Elizabeth Thomas. I have his parents as Thomas Bundy and Mary Alexander but that info came from Rootsweb so not verified. However I then have this Thomas Bundy snr. as a child of William and Ellinor. Not sure if this helps or makes it more confusing but it does make the link to William and Ellinor. You mention a birth certificate for Thomas 1663, this must be a parish record I assume? If this is correct then my (and others) records must be incorrect.
My Thomas 1663 has children:- Nicholas,Elizabeth, Thomas, Joel & Mary. Does this fit?