Other people's trees can be helpful - as a pointer. Then starts the work of verifying for ourselves to see if what they say has some basis in fact. Its 50:50, either its right or wrong.
Unfortunately all too often, someone takes a wrong turn and others see it. Rather than verifiying what they see, some happily just add it to their own tree and so it goes on. Enough people do that and it 'looks' like its writ in stone. Have you contacted any of the tree owners? Maybe they have taken what is on the marriage cert as being true - and though I think its a remote possibility, it IS technically possible that a 20 year old girl had a fling with a sailor twice her age who was in port for a week or so in Newcastle and he sailed off into the sunset leaving her pregnant.
But if you are asking if you should give up,. I am the wrong person to ask :-) I've been searching for my 2x G Granny Mary Ann Brown who was, apparently, born c1817, for almost 20 years now - and still nothing prior to the day she wed my 2x G Granda John Mavin on 26th June 1842. The marriage record says her Dad was called John Brown and that's still all I know. But I still dust her off now and then and trawl through the records, someday something may turn up, there are new databases popping up and I check them, but for the moment her Dad's name (as given on the marriage cert) is all I know. Doesn't stop me haring off following the most tenuous possible lead. In the meantime I have worked on other branches where I have found info.
It aint over till the fat lady sings, and I am not about to even let her on stage while I am still around
:-)
Only you can decide, one suggestion is you document back to your John William, see if there are any clues in the workhouse records when RTL is able to look for you. Ditto for the baptism record. Work on other branches and document what you can find for them.
Read the threads about DNA testing and 'perhaps' that may be a way forward. If you are as sure as you can be about your combined tree, then a DNA match "may" turn up that doesn't fit into what you know and then you can follow that? I have read that sometimes it can break through brick walls such as yours but I have no experience of it at all.
It IS rotten when you think a record you order is going to answer the puzzle and the damn thing arrives and just sparks more questions. Its sometimes the way things go :-(
Boo