I deeply apologize for your frankly ridiculous, under performing excuse of a teacher. This event meant a lot to you and he basically left you stranded in the deep end of the pool which is unacceptable.
"He agreed and wrote it on his schedule that he'll bring extras of everything because they needed them" Is there any way for you to get that schedule? Or prove to his superiors that he marked it down? I don't believe he'll be honest with you about not giving your teammates the equipment they needed.
I'd try going to his superiors with all the evidence you can get, make your case and prove whatever you want to prove. Whether he purposefully bailed out on you or that he cost your teammates the competition because of his incompetent and moronic behavior. Also is there a video of your teammates performance somewhere? Maybe use that along with another team's performance as a comparison.
Honestly though this is just my two cents, either it's a real shame this happened to you and I hope you can get this whole issue resolved. Good luck!