Could you use Bluetooth to play YouTube music?
It sounds like it wouldn't be a great experience, since YouTube probably has features that Bluetooth doesn't support. But does it at least solve the main part of the problem, or does that somehow not work?
(I have a podcast app that I sometimes play through Bluetooth when I can't connect via Android Auto. The Bluetooth version is less good, but it does let me listen even when my cable is flaky.)