How did "Captain" become a term for a businessman who employed prison labor?

Solution 1:

The word captain was never specifically “an honorific for persons who employed prison labor”. It is a more general term. It has always been used to mean the chief, or head, of many types of gangs of men. Your example is typical.

Consequently, the origin of your great-grandfather’s honorific is the same as the origin of the word captain itself, which is ultimately the Latin word caput, from PIE *kaput- (head), so literally head-man.¹

NED attests this usage at sea:

^{1801 Naval Chron. VI. 103 He was captain of a gun at the Battle of the Nile. 1833 M_ARRYATP. Simple II. vii, The captain of the main-top was there with two other sailors. 1859 F. G_RIFFITHSArtil. Man. (1862) 208, No. 1, the Captain [of a gun] commands, attends the breech, primes, points, and fires. 1882 Navy List July 459 Captain of Quarter-deck Men, Captain of the Forecastle, Captain of the Foretop, Captain of the Hold, etc.}

underground (mining):

^{1602 C_AREWCornwall 10/1 Their ouerseer, whome they terme their Captaine. 1757 B_ORLASE in Phil. Trans. L. 504 This very intelligent captain of the mine observes, etc. 1852 Leisure Ho. 632 note. 1864 M_RS. L_LOYDLadies Polc. 16.}

in various trades:

^{1886 Newspaper, D. H., ‘captain’ of Messrs. Davies’ [tailors’] shop, said that he never saw a coat worse made.}

in schools or forms (grades) of schools:

^{1706 Spect. No. 307 ❡ 13 Every Boy is bound to have as good a Memory as the Captain of the Form. 1730 Etoniana x. 156 There was a speech made by the captain. 1825 S_COTT in Lockhart (1839) VIII. 149 A schoolboy who writes himself Captain of Giggleswick School. 1864 Blackw. Mag. XCVI. 226 (Hoppe) The late captain of Harrow . . gives it as his opinion that the small houses have their necessary advantages.}

Notes

1. *kaput- is the ancestor of many other modern English words (http://etymonline.com/index.php?search=caput):
   • corporal, chief (and mischief), chieftain, cadet
   • capital, cape (promontory, such as Cape Canaveral), precipice
   • biceps, triceps, occipital, capillary
   • achieve, capsize, decapitate
   • cap, cabbage, chapter
   • caput
   • even head itself! via OE heafod, PGmc *haubudam