Hi Jo, I wouldn’t advise using a stain at all, you would have to treat the whole beam and it could end up looking a lot worse than it does now. In fact it looks like you have done really good job of removing most of the plaster and now it doesn’t look that bad to me. I’ve got a house with oak beams and when we moved in we removed a lot of plaster off the beams. Like you we found it still left some stains but they have faded over time. We did try using linseed oil but that just made the plaster stain darker and leeched into the plaster on the walls making even more of a mess.

Definitely don’t  sand it, you would lose all the patina it’s gained over the years. If you want to do something I’d go back to the toothbrush (or a small wire brush) and use some water to wet the plaster stain and that will speed up the fading process,

You could fit another beam in front or an L section beam that wraps underneath.

Fix it to the existing using 2-3 recessed screws and plug with oak dowel.