The belt sander and random vibrating sander prove effective. Check out the colour difference between sanded and unsanded areas. It's actually starting to reveal some wood under that dismal grey.

I officially had no idea how to use a belt sander though. It's not as easy as you'd think; you have to keep it steady and apply even pressure in long back-and-forth strokes. If you tip it up on it's edge, you leave slight gouges in the wood, which are undesirable. Not that I did that, Eldest Bro, no way. I became an expert immediately. Or after a few strokes and a quick observation of the expert.

The vibrating sander is a completely different beast. It shakes so much that it's almost impossible to hold on to. The Ol'Dad handles it with careless ease, of course. No problems, and even when it sputters and coughs to a halt (it being about as old as I am and, unsurprisingly, full of dust), he just rattles it a little and it starts up again.

Using both, we manage to get the top looking relatively clean and delightfully smooth. Now we just have to tackle the rest of it.