I tend to avoid asking ENTJs what they are feeling mid-boss. (I mean, it's work, who cares?)
I'd advise playing the logic card with any ENTJ. It's worthy of their respect, and works with my ENTJs really well. As in "it would be more logical to do this." or "I feel uncomfortable because I do not understand the logic of your request." Or "what goal are you trying to meet?"
Another card they like is "this will work better for your master scheme." Of course it only works if this would work better for their master scheme.
Just this week, I tried, "that would take 7 hours, but I did this in 15 minutes and it works just about as well. Can you use it instead so I can finish the other 5 things I have to do?" Worked like a charm.