I'm gonna throw this idea here and see if it gets any traction.

When you first enter Diadem, there should be an NPC that allows you to set your "Objective" on why you are there.

Battle=+1 party member and a 10% stat boost/inability to lot on gather chest
Gathering=Inability to lot on battle chest but your gather chest belong to you

Basically for those who just want to fight as long as the others aren't just out to gather you could have a party of 8 with just 4 members with that status effect but the above is something that would only be applicable in the Ishgard side of Diadem or just Easy/Normal mode.

I feel a simple change like this would help to prevent the hostility created through people with different objectives, if Battle/Gather both want to do different things, they have the ability and those with battle can set themselves to battle and be counted as an additional party member when it comes to getting credit on chest.