Really sorry this happened to you; you have my sympathies. Regarding on getting to the bottom of how this happened, I would start by considering all the possible attack vectors and narrowing down the surface.

Here are some of my thoughts on the situation:

• Where are all the places and devices that could get access into your bittrex account? Could one of them be compromised with malware or trojan?
• Open up your process manager(ctrl-shift-esc) and see if there's any suspicious process running. This isn't a foolproof way to check if you're compromised(eg. if you're infected with a rootkit, it likely be hidden from the OS itself) but it's some place to start.
• You mentioned that the account is shared with a partner. Does he have access to the account as well? Could one of the devices he's using be compromised?
• You mentioned that the bittrex logs didn't show the perpetrator logging in and it could be a bot doing it. Did you check the API Keys list? Did you ever create any api keys before that you can recall? Keep in mind resetting the 2FA deletes all keys there so it probably won't show up now.
• The email notification on login has a "disable your account" link which will basically freeze your account which will stop any further withdrawals. This could act as a "oh shit" panic button.
• You'll have to redo the 2FA again since your video exposed the new 2FA QR code for it.
• Consider using the whitelist withdrawal feature and have it locked to a cold store address you control.
• Consider using the IP whitelist.

Do keep us updated on how this turns out. Good luck.