CrossCrossCross is not impossible. There are 2 things you need to realize to manage it:
1) As per my comment below, when altitude isn't a problem and you need to jump maximum distance, don't jump while still on the platform. Run off the platform, then jump.
2) As someone else pointed out below, there's a tiny ledge straight below the goal.
After that, the rest is practice, timing, and fingerwork.
Crosscrosscross was a bit of a challenge, aye. Took me a while to get to grips with the ideal jump being slightly after leaving the platform instead of just on the edge, as platformers have conditioned us to expect. And then a bit longer for my brain to actually get my fingers to accept it :P
For years I've played games on Kongregate and never signed up. But now I signed up just to applaud the use of Cave Story music. The game is ok, very good considering the time spent on it, the end is a bit annoying considering it can't be muted or quit without reloading the page. The use of Cave Story music, though, makes it 5/5. Reading through the comments, I've seen just a few referencs to this use, and I sincerely hope this is just because it's obvious because everyone is familiar with it. After all, a lack of knowledge of Cave Story in a gamer is a terrible thing.