I've been using cohost here and there and I think now I can explain what I'm looking for, and it's kinda like how forums work.
One of twitter's worst experience issues is how they present the timeline. They have a business interest in presenting tweets in some order determined by your behavior, their advertisers, popularity, and a lot of other weights. You can switch to chronological mode temporarily, but there is a steep price to pay for that: tweets with lots of activity from accounts you follow will appear many, many times and spoil the timeline. Infinite scrolling doesn't help much when scrolling past the same cat picture 50 times. And of course Twitter is designed to keep your attention as long as possible. Not a good combination.
Cohost doesn't have those concerns, but even with just a handful of accounts followed, I am seeing the same post appear multiple times on a single page. So to improve this and make using the site more efficient (with or without infinite scrolling, as has been requested already), you could instead present posts chronologically, and only once per page load or visit. Each time there is new activity, present the new unseen activity first, and hide the rest until the user clicks through to the post.
I think this could really improve usability for people who only use the site once or twice a day like me, and maybe even help avoid some compulsive behaviors and adaptations that people coming from Twitter might bring with them.
I think compressing posts so you don't see them more than once per page would be a very good compromise between the commitment to a chronological timeline and the desire to not want to scroll past the same post six times in a row. If you follow a bunch of people who follow each other, then whenever one of them makes a good post, it becomes your whole feed for a while as they all reblog it from each other (and reblog each others' riffs on it, and so on).
I think UI that said something like "Alice @foo and Bob @bar
Okay well I guess emojis break comments. That was supposed to say "Alice @foo and Bob @bar [reblog symbol] Charlie @baz." I think this would be a pretty intuitive and readable way to present that information, and only compressing posts within a given page would still keep it pretty close to chronological while avoiding having to see the same post over and over. This could also be a toggleable option if some users would prefer the pure chronological experience.
For me, this would be a more useful feature than any manual "mark as read" button or anything, since most of the time I can scroll past the offending posts faster than I could tell the site to stop showing me a given post, and there would be know way of knowing whether there were a bunch more shares of a post coming up or if I'd seen all there were to see.