I'm not sure there is much to made of the east end thing; after all, if the two tunnels had an east end and a west end each, then if the two narrators guessed which end it occurred at they had a 50% chance of guessing the same end. Secondly, the east end is NOT mentioned by Spencer, but is only free-floating in Alabama tradition. Note the sentence:

"Although Spencer doesn't comment on it, it is held in the tradition around Leeds, Alabama, that the contest took place just outside the east portal of Oak Mountain Tunnel."

So when you say

"Lawson and Spencer have in common:
(a) the contest was outside the east end of a tunnel,"

you are putting words in Spencer's mouth.

It's impossible to tell by this account if people say "it happened at the east end/portal" (which would involve the words "east end/portal" and could thus result in those words entering the oral tradition of John Henry tales to emerge in the Big Bend versions) or if they just point out the spot and say "Yup, it happened right there."   

"John Henry fell."

I think it is only common sense that if a person dies from overwork while driving steel, he will fall down first rather than remain on his feet. It is hardly startling for this detail to show up in two versions of a traditional story.

Throwing water on John Henry could be a traditional motif of the legend that did not make it into the song tradition, but it is also possible that in real life, when a railroad worker collapsed of heat exhaustion (as must have happened sometimes), his co-workers threw water on him to revive him. If this is the case, then a railroad worker extemporizing the story would naturally tend to insert that detail. In other words, it could be a traditional motif or a commonsense detail of the occupational culture of railroad workers. In neither case does it make it much more likely that one of the stories is accurate.

It is still possible, of course, that one story IS more or less accurate (the Alabama one) and that the details traveled in oral tradition to the area around Big Bend. I think this would be a firmer proposition if we could show that the words "east end/portal" were used in an Alabama version. But it is certainly a possibility either way.