Sliver was banged out in mid-1990 with a single one hour studio session plus one more session for rerecording the vocals. It was invented in a rehearsal session bare weeks before so it’s a remarkable product of a very specific period of time.
In terms of Nirvana’s musical direction, Sliver represents either the start of the Pixies influenced mode (guitar quiet, voice lead verses, then all out roaring choruses) or, alternatively, an abandoned direction the band was experimenting with.
Slilver was something different. As discussed in the book Dark Slivers: Seeing Nirvana in the Shards of Incesticide, the song was a penultimate effort at a lyrical writing mode soon abandoned. Musically its approach was to start with no guitar, roar in for the first chorus, then keep the peddle to the floor right through to the end of the song. This was unusual. It doesn’t have a stereotypical Nirvana verse/chorus/verse approach. Instead the amplification comes on and stays on.
There are two songs to which it should be compared; Here She Comes Now, recorded shortly before Sliver, and the cover of D7 recorded soon after.
In all three cases the approach is the same, the song reaches a chorus, stamps the effects pedal and never takes the foot off. Kurt had long been a fan of the Wipers so it’s no surprise he would cover one of their songs. The Velvet Underground cover though came about only the request of a record label that Nirvana didn’t want to turn down – potential publicity and new fans not being so common at that time. Nirvana weren’t ruling the world just yet, they barely made any money.
Nirvana didn’t perform D7 in concert until late 1990, prior to its recording for the BBC. Here She Comes Now, however, was performed in concert in May 1990 making it the last NEW song to appear before Sliver was created. It seems possible therefore that Here She Comes Now influenced the creation of Sliver. Curiously, following Sliver, there aren’t many other songs that sound much like it. It would imply that Sliver’s place on Incesticide, a compilation showcasing abandoned approaches, was partly because it really was an experiment the band never followed up on.
Nirvana Legacy 
One thing which you left out was the role of Dan Peters. Both Krist and Dan have said that his presence was instrumental in the creating of this song, and that it flowed out easily. Whether that means they were just jamming differently because there was a new person or something else, I don’t know.
One musical influence of the song which always seemed obvious to me: the Fluid, the connection of the two bands themselves is obvious. But musically – listen to songs of theirs like Cold Outside or Madhouse. And, in a more general sense, the musicality of this song should be located firmly in the contemporary pop punk scene that zines like Flipside loved covering at the time.
I’ve always thought that the drum sound is crucial to a song like that – but, on the other hand, do I think that the song wasn’t mostly formed before Dan Peters was brought anywhere near it? Yup. For sure, end result sounds different! And you’re right, I skipped – oops.