I always saw Maxy as most powerful Imp. or maybe most important one, due to him being foil to Supes, but that Imp in pen would be most powerful on that earth!
Think that you are right about precise wording, as have to command him to do a specific act, not just say stop Injustice league!
Since my daughter is working her way through that JSA run, I just saw the "Say you" "So Cool" switch. It was based on the geneie's name, and there was a story line where he merged with another imp, changing the key words for Jakeem. Then the genie merged with Johnny Thunder, but that seems to be switched back by Doomsday Clock...maybe???