Anyway, at some point Instagram ads (especially the autoplaying video kind, with sound) drove me crazy enough that out came jadx and apktool and I found a beautiful way to inject my own code into Instagram's networking. The code I injected rewrites the API responses before the rest of the app sees them. I can now scroll through my feed without annoying salesmen begging for my attention. I've also enabled a "secret" debugging menu while at it, where there are manual overrides for server-side settings, and there are at least several hundred of them — it's a bit creepy what they're A/B testing, like slightly different wording or different button colors.
The only problem that still remains is that the feed is still algorithmic, and there's nothing that could be done with that with client patches.