Origin and history of "spinning jenny"

The origin of spinning jenny (the cotton-spinning machine invented by James Hargreaves) always seemed to me to be named after a person called Jenny. However, as I was reading Etymology for Everyone by Anatoly Lieberman, the author proposed two origins.

The first theory:

It "is said to have been so named by the [inventor] after his wife, Jenny."

However, it was further suggested that

"It is a 'corruption' of gin, a contraction of engine. Gin would easily suggest Jin, Jinny, and Jenny."

Clearly, spinning can't be disputed insofar that, as the prefix, it comes from the word spin, but my question here is about the origin of -jenny:

Does it mean "engine" or is it as innocuous as it appears?

An article on revolvy.com stated that "parish registers show that neither [the inventor's] wife nor any of his daughters was called Jenny". Could gin be corrupted this much over time? Any help?

Jenny looks very much like a proper name, and the Etymological Compendium: Or, Portfolio of Origins and Inventions says that Jenny was the name Sir Richard Arkwright's wife, not the name of James Hargreaves's wife.

Sir Richard Akrwright was a barber who improved the spinning wheel invented by James Hargreaves and made a fortune as a manufacturer.

Etymonline supports the same view, but doesn't rule out a possible curruption of the term "gin":

• Akrwright's spinning jenny (1783) is said to have been named for his wife, but is perhaps rather a corruption of gin (n.2) "engine."

Gin:

• "machine for separating cotton from seeds," 1796, American English, used earlier of other machineries, especially of war or torture, from Middle English gin "ingenious device, contrivance" (c. 1200), from Old French gin "machine, device, scheme," shortened form of engin (see engine).

The improved spinning jenny that was used in textile mills (Wikipedia)

Okay, I have no proof of this, but it is a beguiling notion that the name could be related to the Scottish term jennie

2. A man who meddles with or assists in a housewife's work
   (Rxb. 1923 Watson W.-B.; Ayr. 1928);
   a man with effeminate habits
   (Uls. 1905 Uls. Jnl. Archaeol. 124, jinny; m. and s.Sc., Uls. 1959). Cf. Jessie.
   
   --Uls. 1901 J. W. Byers in North. Whig v.: Jenny . . . is applied derisively to a man who concerns himself with purely feminine matters, as, “He's a regular Jinny.”
   
   Comb.: Jenny Wullock, a hermaphrodite, a sexually-deformed male
   (Gsw. 1934 E. Partridge Dict. Slang),
   an effeminate man
   (e. and wm.Sc. 1959).
   Used of a castrated bull
   (Ayr. 1959).
   Wullock is a dim. form of Will(iam).
   
   --Ayr. 1887 J. Service Dr Duguid 156: Whyles I was so stawed o't, I wished in bitterness of spirit that auld mother Eve had been a Jenny Wullock.
   
   --Sc. 1935 Border Mag. (Feb.) 19:
   A boy doing girl's work had an uneasy row to hoe, having to suffer the mockery of: Hauf a laddie, hauf a lassie, Hauf a jenny-wullock.

if spinning is seen as a feminine industry (hence spinsters and distaff side) then something as masculine as a machine to help with it, might fall into the blurry male/female hinterland which this Scottish term seems to cover. But there is an equally beguiling notion in the next definition of jennie in the Scottish National Dictionary, which is

3. A cranefly or daddy-long-legs, Tipula oleracea.

and which might be poetically attributed to the form of the Fly Wheel.