This game is so flippin good....Can't get enough. Been stuck on 4-3 for a while (can't get the timing to get past 2 moving spike things) so going back and getting "A" on all the other levels. So good.
Andy C83 did a really nice run through the game and posted it on YouTube. If you're still having trouble, look it up and go to 13:33 in the video -- he navigates the part you're talking about perfectly.
I wound up studying the video for that part myself. I got more deaths from that part than any other. It's a sort of counterintuitive segment there.