* "Milwaukee" wasn't Big Mac, even though (if Levy is correct) it
was also sometimes referred to as "Little Big Mac". As Aventure-Apple states (and Levy confirms), it was a rival (or at least completely indepdendent) effort.
Insanely Great says that it was a grassroots initiative by engineer Mike Dhuey focussed on creating a version-2 Macintosh with internal expansion slots. (And it wasn't even the only other project working on a successor Mac in the time between the release of the original and Jobs' firing.) Jobs likely didn't even know it existed, as it was hidden from him to prevent him from killing it. At some point (according to Levy) this meshed with Jean-Louis Gassée's vision of a high-end Macintosh line which would give power users the things they liked about the PC. He went so far as to get "OPEN MAC" number plate for his car, where 'open' in this case referred to slots.
Insanely Great seems to suggest that Gassée had this ambition even before he heard about Milwaukee/Little Big Mac, but it's not competely clear on that point. In any case, after Jobs was gone and Gassée had been given the reins, he killed off Big Mac and Milwaukee was allowed to become Macintosh II.
* The Apple Extended Keyboard https://deskthority.net/wiki/Apple_Extended_Keyboard with its Model-M based layout was by far the biggest Apple keyboard up to that point and was clearly part of the Macintosh II power-user vision just as slots and colour were. (IIRC it was explicitly justified as making the Mac compatible with PC software.) And so it's no surprise that Jobs didn't like it: https://www.flickr.com/photos/jurvetson/841771 .
* It isn't quite directly stated anywhere I know of, but it's clear that rival visions of Macintosh cost, margins and market share were a big factor in the internal strife. Even back at the launch of the original Macintosh, Jobs had been very unhappy that the price had been set at $2500 rather than $2000 https://www.folklore.org/StoryView.py?project=Macintosh&stor... . There's also a video clip from the '90s, almost certainly from his NeXT days, complaining bitterly about Apple's decision to choose high margins and low market share for the Macintosh, but I can't find it atm. Despite the big screen and the ambitious Unix-based OS rewrite which probably imposed a big RAM penalty, Big Mac's creators evidently hoped (realistically or not) that it would compete for something like the mainstream market. On the other hand, whether or not this was quite Gassée's vision from Day 1, the Macintosh IIs were and remained brutally high-margin, priced to soak those who not only both needed a high-end Mac and could afford one but were also trapped on the Mac platform, while the all-in-one Macs (and even the later LCs, to a lesser extent) were kept underpowered but also swingeingly expensive. It's not a coincidence that Gassée popped up to smirk and leer when the 2019 Mac Pro's prices were announced https://news.ycombinator.com/item?id=20163321 . To be fair, the Macintosh II pricing strategy actually did make Apple a great deal of money, for a while. Meanwhile NeXT was, ironically, in no position to compete for the mass market.