So instead of having the person on chest duty key or destroy the chest, you want to have him call someone else to key or destroy the chest.

For blue chests, you key or destroy XP, Cruor, temps, and time extensions. No communicating on those.
ISL, you leave the blue chest and let your party know that its there; I'm sure they can see where you are and realize that the blue chest that you left is the right chest.

Red chests are key or destroy, no communicating.

For gold chests, you add items to the pool, call-out-and-open or destroy temps, and call out and open key items. The giant, open, gold chest is usually enough of a visual hint as to which chest it is.

Anyone who is checking chests should have keys, and if you're just opening ISL, you should also have keys for that.

The chest system in Abyssea is fine as it is.