re: Opinions wanted - solid slab door battens

Have you measured the moisture content of the pieces?  Unless they are below 15%  (10 would be better), you may never be able to keep them flat, especially since you say that they will cup if you do not keep both sides covered.  A finish will not prevent future cupping if they are not stable to begin with.  Personally I would uncover and either stack and sticker them or  lean them against a wall indoors so air can flow around both sides where they will live and let them acclimate for a month or two to see how they move and measure the MC periodically to see how it changes.  If the MC is high when you build, you may find that they will shrink a little too, on top of warping, which may also create a gap later on as well.