The most obvious thing that I noticed about Nicola Griffith's Slow River was the variance in storytelling styles. Not only are there three different storylines ( Lore's life with Spanner, her work at the purification plant, her childhood flashbacks ), but they are told in three different ways ( third person past-tense, first person past-tense, third-person present-tense ). It was incredibly jarring for me at first, as it went against everything grammar school had taught me about sticking to one style of narration and one time frame. It's still a bit odd, but I've been able to work through what Griffith was trying to do.
The third-person past-tense from Lore's personal life is narration designed to make Lore seem alienated and out-of-place, even from herself; we do not get her POV directly, because she is not the center of this universe. She comes in destitute, is taken in by Spanner, and put into a life far different than the privilege she is used to. Her relationship with the cynical, morally ambiguous Spanner is of a very tenuous nature, and she is very ambivalent to the illicit activities she gets involved in. Even though Lore and Spanner are very intimate physically, the narration style seems to indicate an obvious disconnect between action and feeling.
The third-person present-tense from the flashbacks seems to indicate the same sort of alienation, but the shift in tense indicates the importance of her memory; for Lore, her formative years and trauma are not just recordings from the past, but something so important and visceral that it permeates the rest of her life. Like they say, some memories are so vivid that they seem like they just happened yesterday; with Lore's tragic backstory, this would be very appropriate. The third-person POV continues to keep it alienated from her, though also from us; I can see how getting a blow-by-blow recount from Lore as things like the kidnapping are happening to her would be too painful to read, and for that matter, even harder for Griffith to write without slipping into melodrama.
The first-person accounts from Lore's job as Sal Bird are a bit harder for me to get my head around. I can see how the fact that Lore develops her own agency in the field of biological science helps put the spotlight back on her, as she goes from being a spectator to an active player. However, it still seems like Lore has to accept that there is only so little that she can do in her position; she's still the same person as she is at home with Spanner, even if she is more in her element. It almost seems unnecessary, because while we hear about Lore's feelings in both of the present-continuity storylines, only the POV makes a difference. And there, it's just the semantics of wordplay.
Yeah, it took me a while to figure it all out, too. Once I understood the different settings of each POV, though, I thought it was a rather incredible way of showing the reader when each snippet takes place--within the first sentence or two of any section, you can immediately tell where you're supposed to fit it in to the story. And one thing I would add to your analysis is that the parts that are actually happening "right now," or closest to "right now" are, though in first person, told in past tense, while the distant past is told in present tense. It's like Griffith finally brings us close to Lore by telling the story in first person, but then pushes us away again by using past tense.