I get the same lower pricing as you did using my Android.

Try to price other city pairs . If you consistently get a price difference, then I suggest you don't use your iPhone to book future flights. I cannot explain the difference, other than to say maybe Jeff Smisek had an under the table deal with iPhone.

Suggest pricing economy on those same 2 flights (T) to LAS and (K) to IAH. Towards end of booking, you will be offered a buy-up to First. See if that price is less than what you would pay for the P fare now. You have 24 hrs to cancel & get refund.