Limit shares/retweets. Limit groups sizes. Surface more information as topics/tags/whatever so that users can do more sophisticated filtering themselves or collaboratively. I want to mute my uncle when he talks about politics, not all the time. Facebook already does more sophisticated analyses than just extracting topic information (I know because I work there and I can see the pipelines). Show those results to me so I can use them as I see fit. That's how you make things better. Chronological vs. algorithmic order? Pfft. In fact, I do want the most interesting things out of that set shown first. I just want to have more control over what's in the set.
Sorting something to 1000-th page is censorship. Legally probably not, it's still available you just need to click page down 1000 times but IANAL and don't care.
I don't want algorithms to do any filtering. If someone shares crap every 10 minutes I can always unfollow. Still, I like your idea about manual filtering with tags.