We agree with other folks that think 1 - 2 hours away from a flush toilet is way too far...especially if you have to go in the middle of the night! For dry camping with no amenities, we've adopted the toilet seat/5-gallon bucket/trashbag/kitty litter method. Not the same as a flush toilet, but acceptable with privacy from trees or a tarp.
If a flush toilet is a must, we agree that Organ Pipe is an excellent campground and it offers the added benefit of showers. Another option that quickly came to mind is Mesa Verde National Park. It has some of the nicest bathroom facilities we've ever seen. Mesa Verde has more isolated campsites, whereas your neighbors are closer at Organ Pipe. For later in November, you might consider KOFA National Wildlife Refuge (south of Quartzsite, AZ). There are no, as in zilch, facilities there, but you'll not have neighbors and will have awesome views of the mountains. Drop me a message if you would like more details on where to camp in KOFA as I'd have to do a little research to sort out where we camped there last winter.
One other thought.....Water......Take more than you think you'll need if you go the dry-camping-with-no-facilities route . Throw in a basin for washing up. Feeling (relatively) clean can make or break it for some folks. We can also offer tips on making an outdoor shower (without the use of unwieldy shower bags), replete with hot water and a "stall" (for keeping out the wind and for, if needed, privacy).
Lastly, if glamping becomes something you both like to do and you get out enough, you might consider a cargo trailer for towing behind your Wrangler. A trailer enables you to (a) take all the stuff you'd like to have whilst glamping and (b) you can stay out for far longer. We can recommend a mechanic/fabricator that can custom-make such a trailer.
Good luck and have fun!
Stephanie and Blake Barnard