Another idea / suggestion:
Make the no-time-limit (NTL) option a choice that has to be activated (and agreed by all players) once the game has started, like abandoning a game. In addition, once NTL is enabled, allow any player to expel any other player at any time. Of course, this should not happen among friends, but it would prevent getting trapped in NTL, or the mode being abused by ELO cheaters. (If someone expels you from a NTL game, use red thumbs as usual. If this happens after you accept NTL with strangers... you'll be more careful next time.)
Make the no-time-limit (NTL) option a choice that has to be activated (and agreed by all players) once the game has started, like abandoning a game. In addition, once NTL is enabled, allow any player to expel any other player at any time. Of course, this should not happen among friends, but it would prevent getting trapped in NTL, or the mode being abused by ELO cheaters. (If someone expels you from a NTL game, use red thumbs as usual. If this happens after you accept NTL with strangers... you'll be more careful next time.)