I would temper this somewhat, perhaps the "best F service" to Hawaii for a US domestic carrier.

To the OP: the DFW flights are closer to int'l F - you get sundaes, semi-lie flat seats, tablet entertainment so I would chose that option over the US flight via PHX. Do you have enough points/miles for one F ticket? If so then you could purchase F outright for yourself and earn all of the Avios points and then use miles/points for the other.

As for the lounges: DFW lounges are pretty good - but if you happen to have the AMEX PLT or Centurion card then the choice there is the Centurion Lounge - which puts the ACs to shame.