Summaries are difficult for longfics. It's often so subjective what's going to catch someone's eye, and I definitely don't think yours is misleading. (There was once a fic I passed over for a long time because it had [juggernaut ship] and [other ship I actually care about] both tagged and only [juggernaut ship] mentioned in the summary so I assumed that [other ship] was only a background ship. It turned out to be exactly the reverse and a great fic but BOY HOWDY was that a misleading summary!)

The "In which" summary also works very well. I think the big difference is the "In which" serves a taste of the plot, the quote serves tone, and the "solution and solving" bit serves theme. None of which is more right or wrong for a summary, and it's really a subjective thing which readers are going to be grabbed by which one.

So: do what you like the best!