Joe....darn if you didn't nail it exactly. Did something similar some years back when I left Los Anchorage in the dark at 1:30 and was just passing over Gulkana when the sun rose over the Wrangells a couple hours later. Spectacular and, with due apologies, can't be duplicated, no-how, no-way, in Ewe-stun Texas.
To the OP, I'd offer the same advice as joe b......stay up until you're tired enough that the light doesn't bother you. Make the odd hours part of the adventure. Pick some evening (i.e. midnight or later in the summer) when you're not tired and wander away from the RV...just enjoy the stillness and the quiet, watch the pale pinks and oranges of sunrise and sunset, both between 2 - 4 a.m. and so forth.
Granted, it's not RV'ng, but one of the real joys I find in the summer (even in the southern banana belt of Los Anchorage area) is to fiddle around at the cabin all night long, then hit the sack about 5 a.m.....some of the best sleep of my life follows.