Dry conditions.
I'd go for Panaracer Gravel kings SK 700 x 43c, which come out as 45mm. Very fast efficient tyre.

If it were going to rain for days and i hit mud for a few days, i'd carry Schwalbe Thunderburt 29 x 2.1.

This would save a lot of energy, i haven't done the great divide, but most of it looks dry.