LOL it was the Wizard's path (in my second play through) that I managed to make it through with the busted crate.
I tried for what felt like days (it could have been LOL) before I gave up and started a new game (since I did not know about crate stacking and climbing) and took the Warrior's path where I just had to stay out of the center flame and stay alive after the levers were flipped long enough to get through, so I do believe, with you having made the Wizard's path by just running, that your abilities surpass my own.
Moni