I'm not sure you can have a multi-day layover? With one-ways, I feel like you need to go from A to B as relatively quickly as possible.
Anyway, as a frequent HI flyer, I'd do DFW-LAX-LIH. And the reasoning is simple: wifi and no need to sleep. It's a daytime flight, so I really don't see myself waking up at 6am or whatever to catch the 10am DFW-HNL 763 just so I can go back to sleep at 11am.
Now, as for the return, I would absolutely take LIH-HNL-DFW. That is a redeye, and the 763 biz seat is a delight for that purpose.