Alright, so how do you exactly remove the League Voice overlay from the Scoreboard?

Yeah, I googled to see if anyone else had actually found that setting. Troll patch notes, I guess we got April-fooled with a bit of delay.

Solution found: In the hotkeys menu you have to set the M key to some command/action (for me it was show advanced player stats). Since M is by default the key that expands the voice panel, binding it differently prevents it from popping up apparently.