Need Help with CC2LP1

[Bowman]

I'm stuck on lvl 118: Phantoms and need some help. I got all the way to the end with all the chips, got the ice skates; I need the fire boots and the flippers to get to the exit. I can cycle between fire boots/flippers/skates/hiking boots/foil with the ghost up there but I can only hold 2 items. The problem is I need 3 boots; fire boots/flippers/skates (or fire boots/flippers/hiking boots if I wanted to go out of my way to change to Melinda for some reason) to reach the exit. I have reasoned out all of my moves and they all seem necessary and the level seems impossible. So I'm missing something big. Can anyone give me a hint without giving me the answer?

Thanks,
~Bowman