OK, so I went through the rest of this painful Dickens edited article, and it's all culled from LA Smith. Here are the rest of the chanties noted:

HANDY MY BOYS
BLOW THE MAN DOWN
REUBEN RANZO
UP A HILL
PAY ME THE MONEY DOWN (orig. from the 1858 Atlantic Monthly)
HILONDAY
BONEY
HAUL AWAY JOE
SHENANDOAH
OUTWARD AND HOMEWARD BOUND (another variation)
and some forecastle songs like THE MERMAID