Weigh the risks and go for it!
Certainly a higher mileage vehicle may be more prone to a failure/breakdown. It's only a matter of time before something breaks right? =) I've run most of the TAT on a KLR and drove MS and AR in a Nissan Frontier. The truck had 192xxx miles for those trips.
Regardless of what you drive/ride, I recommend a SPOT or similar device whether you're alone or even with others. Portions of the TAT are remote with no cell service. Sorry, you probably already know this but just throwing my $.02 out there. My son and I stuck the truck in a ditch in AR with no cell service and no other traffic seen for hours. We got unstuck and continued the trip without too much fuss. Later I made the commitment to get the SPOT. Realizing that if a serious injury/event were to occur the SPOT would at least allow a chance for summoning help. The SPOT is part of my kit since 2008.
Anyway, have fun! Will you run the TAT in sections or go "all the way" in one run?