Well, I dont think this is going to be as dramatic as you think. Today, sunset in Dallas is 8:19p and in Vancouver, 8:46p, so you only have 27 minutes difference although you do "loose" 2 hours in route. I just dont think you are going far enough west for it to be all that much of a big deal.
Now get on a plane in Dallas and fly to Anchorage (in a similar timeframe), you will truely get a perpetual sunset, not so much because you are flying west (because you cant keep up with the earth's rotation), but because you are flying way north. Sunset in Anchorage today is 10:36p, sunrise tomorrow, 5:20a.