The same thing social networks did before.
If I subscribed to 1000 people, show me whatever the hell they wrote, all of it, in chronological order.
Don't show me what my friends wrote on other pages, if they think that's important of interesting, they will link or share manually.
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.