Taking John's list(s), I have done some sorting based on the form/style as I see it. My categories ignore what any writers have said the function of the chanties were. I am basing them on my own analysis and experience singing them only. Other opinions welcome! Oh, and I'm not adding (many) titles, just sorting John's.

1. Call-response-call-response form (with the 2 "pull points" per response):

"Yankee John, Stormalong"
"Stormy Along, John"
"'Way Stormalong John"
"Stormalong, Lads, Stormy"
"A Long Time Ago"
"Goodbye, My Love, Goodbye"
"Roll The Cotton Down"
"Roll The Woodpile Down"
"Sally Brown"
"Knock A Man Down"
"Huckleberry Picking" / "We'll Ranzo Ray"
"Hilo, Johnny Brown"
"The Gal With the Blue Dress On"
"John, Come Tell Us As We Haul Away"/ "Mobile Bay"
"Gimme My Banjo"
"Run, Let The Bullgine Run"
"Walk Along My Rosie"
"Coal Black Rosie"
"Bunch O Roses"
"Way, Me Susiana"
"Round The Corner Sally"
"Sister Susan"/"Shinbone Al"
"Walkalong, Miss Susiana Brown"
"Dixie Land" / "Sing A Song, Blow-Along O!"
"Bully In The Alley"
"Fire Maringo"
"Blow Boys, Blow"
"Poor Old Man" / "Dead Horse"
"John Cherokee" (Colcord)
"Hilo Come Down Below" (Bullen)
"The Bully Boat"/"Ranzo Ray" (a) (Sharp)
"Tommy's Gone Away" (c Sharp)
"Whisky Johnny"
"Billy Riley"
"Hello, Somebody"
"High O, Come Roll Me Over"
"Where Am I to Go, M'Johnnies"
"Roll, Boys, Roll"
"Ranzo Ray" (c)
"Hello Somebody"
"Can't Ye Hilo?"
"John Kanaka"
"Haul 'er Away" (a)
"Haul Away, Boys, Haul Away"
"Walkalong, My Rosie"
"Do Let Me Lone, Susan"
"Sing Sally O" (b)
"Essequibo River"
"Hilonday" L. Smith
"Pay Me the Money Down"
"Walkalong You Sally Brown"
"Hilo Boys Hilo"
"Tiddy High O"
"Heave Away Boys, Heave Away" (b)
"Sister Susan (Shinbone Al)"
"Miss Lucy Loo"
"Heave Away Boys, Heave Away" (a)
"Tommy's on the Tops'l yard"
"Good Morning Ladies All" (b)
"Won't Ye Go My Way?"
"Tom's Gone To Hilo"
"Hanging Johnny"
"So Early In The Morning" (a) / "Bottle O"
"So Handy, Me Boys"
"Leave Her, Johnny"
"Across The Western Ocean"
Across the Rockies
"Hurrah, Sing Fare Ye Well"
"Hoorah For The Blackball Line"
"Lower The Boat Down" (Colcord)
"A Hundred Years Ago" (a) (b)/ "'Tis Time For Us To Go"
Poor Lucy Anna
Round the Bay of Mexico
Doodle, Let Me Go

SUBCATEGORY - These have the same form, and they probably would have worked for cotton-screwing as such, but aboard ship they are typically too slow for halyards. So, I reason, they were adopted for slow, a-rhythmic tramps around the capstan. Their shipboard function, however, does not keep them from being relatives of the others. The same process could happen to any other the above if rendered very slowly. And even the ones in this category could be sped up (e.g. the popular fast, halyards version of Shallow Brown):

Southern Ladies (fr. Sharp)
My Dollar And A Half A Day"/"Lowlands"
"Mr. Stormalong"
"Shallow Brown"
Shenandoah (and variations)

SUBCATEGORY - Here's one that strikes me (a hunch) as something fitting the form but being a creation of later days:

"Serafina"

SUBCATEGORY - And here are two that have a slight irregularity in the form, but which nonetheless could have worked just fine for cotton-screwing. I hypothesize that because they had that irregularity in timing, they could cause slight confusion at halyards, so they were used for capstan, where the timing didn't matter:

"Good Morning Ladies All" (a)
"Stormy Along, John"

This "Category 1" could be broken down further. I think subgroups would cohere that would show such possible groupings as: Southern States songs; Caribbean songs; earlier songs; later songs based in the paradigm of the earlier songs; etc.

In this category the songs are all those that I feel are practically unmistakable as chanties (as opposed to another genre). And the vast majority ("Serafina" might be an exception) seem to me to have a strong African-American connection.

I'll do other categories later.