I think the crazy glowing wall of doom at the end of the timeline display gives some new insight into how the rest of the Trolls think. As said, at the point in time Sad Karkat is posting from, Sollux is still deciphering what went wrong outside of their own session, and they don't know about the kids yet. It's hard to judge a sense of scale from that graph, but it looks like the Rift could be as little as a day or so into Sad Karkat's future. (The exact timeline has some hints - Terezi trolls the kids forward in time, at whatever pace she wants. She gets Sollux to decode the rocket-pack code for John, which presumably took quite a bit of time, and that was after the trolling had already begun.)
But anyway. So, the Trolls think, or at least Karkat and Sollux think (see Sollux's conversation with Kanaya back when), that their universe is going to end in short order. Sollux throws a big fat sulk over the matter, but Karkat, Terezi, Tavros, and Kanaya step up to troll the kids and try to figure out what's going wrong. There's also whichever of the remaining troll-girls who came up with the trolling plan but didn't want to participate - it's not clear who that is, but Vriska's horn was visible in that teaser shot. Which also means that at least Gamzee, Eridan, and Equius, and probably Feferi, Nepeta, and Aradia (who Karkat keeps calling thoroughly bonkers) all more or less decided not to partake in what may be the answer to their salvation. We know most if not all of them are still alive in the future, so one wonders just how hopeless they think the situation is.
And now I think back on it more, Karkat decided to troll backwards, to figure out what the kids screwed up. He mentions this, and that he still hasn't figured it out, long before Jack gets the ring, which from Karkat's perspective is long after. Apparently, he also degenerated into such a belligerent wreck that he was almost incomprehensibly mad in John's kinda-recent past, when he changed his handle. Which all means by extension, that from whatever point he started trolling John in John's future all the way to John's past, neither Karkat nor any of the other Trolls helping him ever found what they were looking for.
Y'know, I think I really do feel sorry for Karkat now. This is what an inherently angry boy looks like he knows there's no point anymore. When he thinks there's no hope. And now that I give it a second look, he may well be right. Which would be a real damn shame if the Trolls exit stage by way of their universe shorting out.