Apparently there was a major craze for Homer-translating in the 1860s. Matthew Arnold wrote an influential paper on it, which lead to controversies, and it became a significant intellectual topic of the decade. Apparently, there was a sort of society of people who hung out at Tennyson's house and argued about Homeric translation - including Tennyson, Arnold, Palgrave, and the Prime Minister, Gladstone, as well as various poets and academics. One of the things they debated was whether to go with "Zeus" or "Jove". If you look at translations from this era, some go one way and some the other, but from that point on they tend in the direction of "Zeus". This 1860s era would match CJS' findings.
So I think that the key was just people starting to look at translation critically. Until Arnold kicked off that round of interest, the Iliad in english was synonymous with Pope, with a side-order of Chapman and Dryden for the particularly erudite, so naturally any other translation that did appear paid very heavy homage to those versions - if you think people got upset today about making the ghostbusters female, imagine what would happen if someone desecrated one of the most sacred works of English literature by changing all the names to new names nobody had ever heard of!
Specifically, the earliest I can find with "Zeus" is J.H. Dart's translation from 1862, written in response to Arnold and using Arnold's suggest metre - though I don't know whether Arnold's paper specifically comments on the naming issue.
"Hades" was around longer, presumably because it was a place, which "Pluto" never was. Although it's amusing to see translators struggle with trying to avoid using 'Hades' as a placename. From Wikipedia we get (for the first mention, where Achilles hurls the souls down to Hades):
"that invisible cave that no light comforts" (Chapman)
"the Stygian coasts"
"Shades of Night" (Dryden)
"Pluto's gloomy reign" (Pope)
"the regions of death"
"Ades" (finally - Cowper, 1791, noted for his literalness)
"the shades" (ah, a Pratchett fan!)
"the realms of night"
"the infernal regions"
"Pluto" (Brandreth, biting the bullet)
Before Buckley, 1851, finally gives us modern "Hades", which almost all subsequent versions abide by (Derby tried "the viewless shades", but you can get away with that sort of thing when you're the Prime Minister, as Trump didn't quite say). Kudos, however, to FW Newman, who went for the far more pretentious "Aïdes" instead. On the other hand, Newman also had the bodies of the dead being eaten by "fowl", so...
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!