Thanks, Andrew, for that excellent summary of the evidence (or lack thereof) for the co-identification of the five John Bishops.
In my opinion, your analysis demonstrates that it is unlikely that John Bishop of Stamford (and probably Taunton) and John Bishop of Holway (and Oxford and possibly Batcombe) are the same person.
Unless additional evidence comes to light, I think that John Bishop-2996 should be disconnected from the current parents William Bishop-7183 and Alice Dunning-2939. There is not enough evidence for even an "uncertain" status.
Thanks for taking the time to document this so thoroughly, it will provide an excellent starting point for further research into the origins of John Bishop of Stamford.