I assumed that Amelia had had John with the man she married but as they weren't legally married at the time of his birth, his father's name couldn't be entered onto the birth certificate.
The father's name
could have been entered on the certificate, but only if he was present at the registration of the birth. If your assumption is right, they could have been under the same misapprehension - or it could just be that he was unable to attend.
However I do think it likely that John's mother was Ellen. It could explain why they waited as long as possible before registering the birth, there may have been lengthy discussions on what to do for the best. The baptism is another matter. The priest may well have been aware of the situation, so they wouldn't have got away with attributing the baby to the wrong mother. As others have said, Helenae is the Latin form used for Helen, Ellen and Eleanor. Those names are somewhat interchangeable, I have one ancestor who is recorded under all three at different times.
I think the ID of John as "grandson" and not "son" (of Amelia) in that first census is quite telling.
If Ellen was mature for her age, then she might certainly have been capable of bearing a child at 12. It's not common, but it does happen, and there was little in the way of contraception available then. (I did not know until reading her obituaries this week that Aretha Franklin became pregnant at 12 and had a child at 13, and another at 14.)
It
could simply be a mistake on the baptism register, but as you have seen the original and there doesn't seem to be much room for confusion with only one baptism on that day, it seems to be less likely. Hopefully something may turn up one day to throw a bit more light on this. In the meantime I completely understand your reticence about revealing names and places.