I've been getting interested in these "firemen" songs as sources for chanties, and poking around a bit. I'll make a couple-few posts.

More references to the "Sailor Fireman" song )for lack of a better title) from above:

[It is necessary to dis-ambiguate this from other "Fire Down Below" songs. For instance, it seems the one on the following pattern was existing shipboard quite early :

Fire! in the main-top,
Fire! in the bow.
Fire! on the gun-deck,
Fire! down below.

in "Burton's Gentleman's magazine and monthly American review, Volume 5", Oct. 1839]

A dramatic scene in BENTLEY'S MISCELLANY, vol 4, New York, Sept. 1839, taking place in a steamboat. Here's the song.

"THE STOKER'S CHANT.
The ebben tide ib floating past, 
   
Fire down below ! 

The arrival time ib coming fast.
Fire down below! 

Racoon cry in de maple tree,
Fire down below ! 

The wood ib on fire, and the fire a sea,
Fire down below ! 


Oo a oo oh ! fire down below !"

Next,

WE FOUR, by Laura L Rees, 1879. School-girls from Boston were heard singing it at work! Here's the passage:

We had also a party of school-girls on board from an institute near Boston, under the charge of Professor B. and wife, and they brought with them the pent-up fun of the last six months, and it evaporated during their voyage. Their girlish voices were often heard in the beautiful melodies of Sankey, and the captain invariably styled them the " Sweet Bye and Byes." One day, under the superintendence of Captain H., a retired sea-captain, these young ladies hoisted a sail, while the crew stood back and watched the performance. The song, to which their manual movement was an accompaniment, was something after this fashion:

Were you ever down in Baltimore?
Fire down below!
Dancing on the sandy shore?
Fire down below!

chorus.—I'll pull this time,
But I'll pull no more ;
Fire down below !
Pay me my money And I'll go ashore,
Fire down below!

Were you ever in Mobile Bay ?
      Fire down below! 

Picking cotton by the day ? 
      
Fire down below !"

There were several more stanzas appertaining to other seaports of the United States, but as Captain H. was an improvisatore, and varied his solos to suit himself, the two I have given are a fair sample of the rest.

Last, on pg 18 of WHITE'S ETHIOPIAN MELODIES (1854) we have the minstrel version text of the song (i.e. as harvested by Hugill).

Fire Down Below (minstrel)
[My link's not working properly -- it is directing to yet another "fire down below" in the collection. Please go to pg 18.]

Incidentally, Hugill's text is defective in a couple spots, and this one provides the fix.