I restored a cedar T&G ceiling in an atrium that was water damaged. The stains are water soluble tanins that have run and dried into rings and drip lines. Sanding may take them out, but your will deal with the dust problem. Sandblasting will leave a very textured surface and may not solve the stain.
I used Behr wood and deck cleaner diluted in water, and applied the material liberally with a masons sponge, scrubbed lightly, then wiped off to leave a damp surface. The tanins re-distributed evenly and left a fully restored, clean natural surface. Try this method on a small area and see if the results are what you are looking for. The trick is, you can't leave a leading dry edge for tanin to accumulate. So work across the entire length of about 4-boards at a time, then move to the next 4 rows and the next, working down the ceiling toward the low wall.