Yup I tried that.. didn't work for some reason. It would only accept my full Google password, which given I use a password manager is not the most enjoyable thing to slowly tap in.Did you try using an app password instead of disabling 2FA? Sign in with App Passwords - Google Account Help
I'm in a loaner Model 3 for the next month or so whilst mine gets sorted out after getting hit. I'll go down and try to log in using this method and see that that works.
I'm sure app passwords used to work on other things like Outlook, etc so don't entirely know why it didn't work in the car. Perhaps they are not allowed on browsers that considered "weak".
It's possible the "Allow insecure apps" setting change did nothing, and it was disabling 2FA that made it work, but I did both changes at the same time so can't be sure. All I know is that the following morning I was able to log in to the native YouTube app.