A Google Books search doesn't turn up only one example of "stick in the mud" or "stuck in the mud" used metaphorically in the 18th century: an item in The London Magazine of 1733 that lists, as one of 14 "Malefactors [who] receiv'd Sentence of Death" at the end of the December 8 sessions at the Old Bailey, "John Baker, alias Stick in the Mud, for breaking open the House of Mr. Thomas Rayner, a Silversmith, and stealing thence Plate to a great Value." I couldn't find any instance of "stick in the mud" from the 19th century involving a situation connected to criminality.
As for the doomed Mr. Baker, it is by no means clear that he owes his alias to a stubborn adherence to a life of crime rather than, say, to his being what we would now call "slow on the uptake." The fact (developed in the Phrase Finder article that the poster links to) that two different criminals tried in London in late 1733 were known by the alias "Stick in the Mud" suggests that the sobriquet may have enjoyed a brief vogue; but whether that alias came from the criminals' associates or from their government prosecutors is unclear, as is the precise meaning that Londoners in 1733 attached to it. In any event, I suspect that by the 1830s the expression "stick in the mud" was understood to refer to fuddy-duddies and slowpokes, and not to incorrigible outlaws.
The earliest 19th-century instances of metaphorical use that I could find in a Google Books search of "stick in the mud" and "stuck on the mud" involved the latter phrase. Here are the earliest two. From a review of "The Pleasures of Human Life" by Hilaris Benevolus in The Literary Panorama (1807):
Mr. Beresford, who, by the bye, has been happy enough to postpone his new "Miseries" for a time, may congratulate himself, with Falstaff, that "he is not only witty himself, but the cause of wit in other men:" if we had not bad [sic] his "Miseries," we had never had these "Pleasures:" if we had not been "stuck in the mud" in his book, this Mr. Benevolus had not helped us out; if we had not felt Beresford's "wasp at the bottom of our boot," Benevolus had not pulled the boot off: not that this work is the echo of the former; unless indeed we compare it to the Irishman's echo, which when asked, how do you do, Pat? answered, very well, I thank you!
From the Monthly Mirror (July 1808):
Up rose Mr. —————, when Dallas sat down,
And stammer'd and stuck in the mud like a clown.
"Nay give him some law," cried a friend, "and he'll plead—"
"Pray do," said the Judge, "for he wants it indeed!"
In both cases the notion is of being trapped or exceedingly slow-moving (in mind).
The phrase "old stick-in-the-mud" pops up (and flourishes) in the early 1830s. Here are the first three instances that a Google Books search finds.
From William Ellis, "Miru and the Man-Spirit," in Fraser's Magazine [London], volume 3 (April 1831):
Spirit! pray what are mortals about?
Are kings hunting conquest, or lame with the gout?
Do they see in their subjects their own flesh and blood?
Answer me quickly, old Stick-in-the-Mud!
From "The Simpkin Papers" in The Metropolitan [London], volume 3 (January 1832):
Isn't he a priest of the real old stick-in-the-mud religion, that was established in Ireland before Orangemen were heard of, and will flourish when they're all drowned in the Dead Sea?
From "Our Birds," in The New-England Magazine [Boston], volume 2 (April 1832):
There is a great, awkward, long-shanked fellow, called a HERON, whom you may see, at times, standing on the shore, or the edge of a marsh, stiff as a poker, demure as a quaker, and, to appearance, most stoically and heroically bent upon doing nothing. Hour after hour you behold him keeping his station immoveable; do not imagine, however, that this moping dunderpate is asleep. Though his chin is sunk upon his breast, though his long neck is doubled up, and lying mightily at ease, depend upon it, old stick-in-the-mud is wide awake; his eye is bent upon the waters, his mandibles are set for a quick snap.
Interestingly, the expression "old stick-in-the-mud" appears in both London and Boston within a 12-month period. John R. Bartlett claims "stick-in-the-mud" as an Americanism in his Dictionary of Americanisms, Second Edition (1877):
Stick-in-the-Mud. (Pron[ounced] stickneymud.) Very common for a slow, inert man; also used for "Thingumbob," "what d'ye call 'em," or a name you can't remember. "Come, old Stick-in-the-mud, and give us a lift."
But despite the term's being "very common" in 1877, the first edition of Dictionary of Americanisms (1846) doesn't include an entry for "stick-in-the-mud."