Tuna,
You think like I do about traveling with the TC. Isn't there a truck stop in Kayenta? Shinney up to some trucks. If not can you just park in front of the restaurant, tourist attraction or gas station getting there late and leaving early? Then there's always in front of the Trading Post in Tuba City. Just keep moving till it looks right. I was excoriated over on the Boondock forum for suggesting this as an alternative way to travel.
My other suggestion is to drive a while into the night and pick a lonely dirt road that you hope will have no over night traffic and just hole up for 6 hours. I've done this over and over again coming across Nevada, Northern Arizona, and Utah. If on an interstate the offramp is called, "Ranch Road Exit". There are many.
Before we purchased the Lance, my son and I were coming back from Moab on hwy. 70 and eventually hwy. 15. We pulled off at a "Ranch Road Exit" with the Dodge flat towing my jeep. Not surprisingly, there were a few 18 wheelers scattered around with engines idling. We plopped our bags on the ground about midnight and it started to rain. Oh no. We quickly got out the two folding lawn chairs and I put all my tools on them so they would hold up a plastic tarp that covered the two of us. It was a short night, as we got up early, packed up and made it down to Cedar City to have breakfast before heading to L.A.
There's always a place to bivouac, sometimes in plain sight, sometimes not. Even your 71 year old eyes will see. (I'm 73, so I can say that)
jefe