George,
We're also the proud owners of an '87 E34. I was so inspired by your original post, that we resolved to do something about it. Actually, when we removed the original curtains to have them replaced, we discovered lots of black stains and some water damage around the portlights and in the v-berth, on top of the lockers. Taking the advice of those wiser than I, we sanded until we choked and then we sanded some more. We ended up doing the entire forward cabin and the top sections in the salon where the ports are located. You can remove the black stains and the mitigate the water damage. We sanded, aggressively, then we used fine brass brushes on the affected spots and for thoses that were more stubborn, we used a one-step teak cleaner. We sanded some more and then wet everything down (cut donw on the dust), used several tack rags and began to apply Interlux Goldspar Satin 60. We sanded between coats. We stopped at four coats and we're very pleased with the overall results (we followed the mfgrs. specs). It was a very labor-intensive process; but worth the effort. Only problem now, everything we didn't redo looks like it needs to be redone!
Good luck.