I can't imagine any cassette wearing out in anywhere near the distance of a TA trip. I also find that chains last me long enough to not need replacement on a TA length trip.
Unlike Patrick the three of us still had the same chains we started the TA with at the end and on the next several thousand miles of riding. I think I did 4200+ miles on the TA, 800+ miles on the Santa Fe Trail, 1000+ miles, on the southern portion of the SC route, and 1300+ miles of the Pacific Coast on my original chain. There was also a bit of riding around home so the chain had maybe 8000 miles on it at last check and was still under the requisite 12-1/16" for 12 complete links.
To be prudent, I'd say check the chain every couple thousand miles and replace it only when it measures 12-1/16" for 12 complete links. That said I didn't bother on the TA when I started with a almost new chain.
BTW we used White Lightning on a portion of the TA and hated it. I never saw so much waxy buildup in my life. It was bad enough that we had a shop clean them in a commercial degreaser. We then switched to Boesheild T9 which we found to be much better. Our chains stayed clean, shiny, quiet, and free of waxy buildup. We also didn't miss the messy calf tattoos.