You have not thought through your offer. Instead of talking about leaving ET. Make it a real trade about money. I have done this before when someone has questioned my trades. They have lost the bet and had to me through on pay pal.
Instead, this is what I suggest, for 1 day, both of you post real time calls. Each call can be only for 1 contract either long or short. Then you back up your calls with a broker report showing entries and exits which is easy to do on for example NT.
Choose a bet size you are both willingly to pay off. If you are both super traders, you could do $ 1,000. If you are both noobs, you could bet $ 10. Whoever loses must send that amount to the other through PayPal.