Note that if you have exposed joists, you can attach the climbing wall studs directly instead of bothering with stringers running crossways.

If going perpendicular to the joists, you can pick an appropriate joist, cut the studs to lean right against it.

If parallel to the joists, just run each stud up one side of the joist and screw. Then your wall will have the same spacing as the ceiling. Will use less material and be simpler and stronger.