What is the on-center spacing of the rafters/beams…what is the distance between them?

For a backer for the drywall, make a structure out of the 2x4s that looks like a ladder.

The long ‘sides’ of the ladder will be nailed/screwed to the inside faces of the beams/rafters, and held back from the face of the beams to provide for the depth of the drywall. The ‘rungs’ of the rafters will provide additional support for the drywall.

Assemble the ‘ladder’, then fasten it in place.

Instead of having the drywall flush with the face of the beam, consider holding it back a half-inch to an inch or so. The shadow line will help hide and irregularities in the construction and will provide additional depth for the eye.