Comparing all the versions, it is clear that the similarities far outweigh the differences, but the differences identify them. However, verses creep from one version to another, get changed, and creep back.
It is an oversimplification to state that the "Cosher Bailey" verses are historic, and usually in the past tense ("Cosher Bailey had a sister; Laughed...) while "Did You Ever See"(Was you ever saw/ Have you ever been to Wales) is present tense "I've got a cousin Daniel and he's got a cocker spaniel". But it is a simplification which generally works.
However, all the Cosher Bailey verses seem to deal with Cosher or his relatives, whilst the other versions allow people to add verses about their own (fictitious) relatives. Clearly, any verses can be slightly re-written and cross over to another version.
Much is gained and lost by the aural tradition. Verses heard once can easily change, as in " I know there was a verse about a rugby player, but I can't remember the name, only the punchline" (or remember the name but not the punch line). Hence:

Oh I've got a cousin Rupert, He plays outside half for Newport
They think so much about him, That they always play without him.
                and
Oh I've got a brother, Kelly, Who plays rugby for Kidwelly
In a game against Llanelli, Someone kicked him in the belly.

I've deliberately shown these as two double lines to show how easily the two halves of verses could be switched without affecting the song.

There is also a tendency for the words to be rendered in a 'Valleys English' style. This may be the original form, but it also seems to be done for effect. One of the main ways this is done is in the use of idiomatic verb formations, which, by their very use identify the version as being from S. Wales. e.g.
Oh, I've got a cousin Anna, And she's got a grand piana,
And she ram aram arama, Till the neighbors say "God Damn Her."
(or, She plays hammer, hammer, hammer, bloody hammer, hammer, hammer)
        can sometimes be heard as:
Oh I've got a cousin Anna, She do play the grand piana
She do also play the fiddle, Up the sides and down the middle.

The version from "Why was he born so beautiful...." clearly has been collated quickly. It has no starting verse as such, and the first verse quoted:
Oh, I got an Aunty Sissy, And she's only got one titty,
But it's very long and pointed And the nipple's double jointed.
          I have heard as Aunty Kitty, which provides the rhyme. However, Aunty Kitty is also seen elsewhere:
Oh I've got an Aunty Kitty, And she plays for Cardiff City (Association Football team)
But when it comes to rugger (Rugby football), She's a dirty little bugger/player.

This highlights another source of variations. I often heard this song sung on rugby trips, and on church outings. On church outings, and in the presence of young children, it became standard to 'fudge' the rhyming punchlines, hence "she's a dirty little player". But the revisions become standardised, giving us yet another set of verses.:
Oh I've got an uncle Russ, And he drives a motor bus.
And when you press the bell, OH the bus it goes like...lightning

Oh I've got a cousin Drake, and he thought he was a snake,
He was sliding through the grass, So I kicked him on the ..Elbow

I'm sure there's much more yet to be said on this subject, but for now this is my two penn'orth

Nigel