I've never hunted the Lincoln National Forest, but there are a lot of places and public land in New Mexico for a choice. The best thing to do would be to do some map research where you plan on going, and pick a few spots out that you think there will be turkeys in case the first location or two doesn't work out. In terms of how different they are, you can use many similar strategies as Easterns on them. The biggest difference really is to lose the small woods mentality. You may have to cover a lot of ground to find where the birds are.
The Lincoln National Forest is supposed to have practically the best turkey population in the state besides maybe the Gila National Forest, but the bird densities are much lower out here per unit of forest compared to the East Coast. If you can get in an area with sign that's a start, but the difficulty with these birds is that they cover a lot of ground in a given day. Finding areas they want to be is essential, and difficult with the amount of ground you have to work with. Realistically I would mainly work with your scouting before the plane lands using maps to give you a bit of a head start and rely on sign from there.
