I would do it just like a wood floor is done, because it's super effective protection and it lasts. Ever bought wood flooring? It is often stained on only the top surface, and the hard poly finish is also applied only to the top. And it lasts for years under foot traffic.
Your job is a porch ceiling, which will be protected from the rain and direct sun, so the best approach is to stain all your individual boards sitting on sawhorses (use a short-nap roller, apply the stain, let it sit for 15 minutes, and wipe it all dry with lint-free cloth). After the stain has completely dried, roll on gloss or satin polyurethane. The water-based stuff goes on milky but dries clear and hard. Take care to not leave blobs or puddles of poly on the surface or on the tongues.
Let the poly cure for 24 hours, and then install it (cut it to length, fit the sticks in, taking care to stagger the joints in a random pattern, and use a pneumatic 2" finish nailer). Don't worry about the cut butt joints not being finished; it will not be a problem.
Watch a few wood floor installation vids on YT. It's pretty much identical--except you shoot nails with a finish nailer (not a floor nailer) at a back angle through the tongues of the boards.