But predicting out real world chaotic orbits a few years in advance to the required precision is fairly trivial. You only really need high precision to line up a slingshot for the next slingshot not the slingshot after that. A last minute correction of 1 mile per hour * 1 month ~= 720 miles.
You're right, the real problem with predicting trajectories through those "keyholes" [1] isn't solving the dynamics equations: our numerical integrators are more than good enough. The problem is we can't measure the initial states with enough precision.
I've been getting the itch to go deeper into KSP after a scratching the surface of the first one (simple landing on Mun). I was considering buying 2. What's your review against playing KSP 2?
Two still has bugs that effect basic gameplay. E.g. the game being in the same state when you reload as when you saved.
The reviews have been so universally negative on KSP 2 that I haven't bought it yet. Anything I'd say would be hearsay; you can go read the reviews yourself. My impression is it's standard enshittfication: some asshole MBA saw a company that wasn't as shitty as it possibly could be yet, so they bought it, fired/drove out the original team, and made a cheap-ass knockoff 2nd game hoping the laurels of the first would drive sales long enough for them to make some quick bucks before buzzing off to parasitize another company. The exact details may be different but it's basically the same story happening over and over and over and over and over in our dystopian cancerous capitalism. We can't have nice things anymore.
As with most discussions of orbital mechanics, the best advice I can give if you want to learn more is: play Kerbal Space Program (1, not 2)