There's also "The Jolly Trades-men" in 'Pills to Purge Melancholy' [tune, "Jamaica" is B238 on my website (ABC and MIDI)]. A manuscipt copy is accompanied by the Jill of All Trades one that's in Scarce Songs 1 on my website as "Fit for any man".
"Tom of All Trades" is ZN1838 in the broadside ballad index on my webesite, and see ZN99.
"Last Christmas 'twas my chance" (Scarce Song 1) is probably the 'Dance of all trades' that replaced the stage jig in 1622 (See Baskerville's 'the Elizabethan Jig')
I think I have a bawdy version of the "Dublin Jack of All Trades", but I can't find the little green book that it's in.