Maybe you could do a Flashpoint like event in game. Make the reboot part of a story line.

Have something happen in the current game(s) that lead to the 2020 'verse getting a reboot. You could even make a new, though intentionally short game just to play the event out. This way not all of the current game history has to be erased. [@BlackSam3091] could keep The Outsiders going basically as is (maybe needing to make minor history adjustments) if that's what he wishes to do, and [@The Kid Lantern] could do the total reboot/restart of the Young Justice game. [@Endrance]'s Queens of Coast City can stay unaffected. Legion could either be rebooted or continue as a team knowing the universe has been changed...