[Zeke]

Steve, there is too much grain and unevenness there to use a screen. Basically a screen is a mesh coated with abrasives. It's not much different than sandpaper, just better and will glide over long swoops and valleys. It will take the top 10 to 15% of your floor off and leave all the depressions, dents and stains.

IDT you want to do that. I would, however, rent a buffing machine with a scrub brush like used on vinyl tiles in offices and stores. There are a lot of cleaners that will bring out the buried dirt, but plain ol' TSP will do the best job. Not too strong either and not an excess of water.

Here's how I would tackle it: using a floor mop and ringer on a good sized bucket, I'd swab the deck sailor style followed by a couple of passes with the scrubbing buffer. Immediately after use the mop and ringer to pick up as much water as you can. Don't let it sit if possible.

Then either hit it again or rinse with again a minimum of water. The color of the rinse water will tell you how you are doing. Then again, immediately use towels to dry the floor as best you can and put some fans in the room with the windows open. Do some closets first doing all the steps.

Once the floor is completely dry it should be lighter in color. At that point you can use a colored wax or a natural wax. Keep the buffer around for this stage and use a bristle buffing wheel to polish the floors.

There is an intermediate treatment that you could do which I'll loosely call in your case, French polishing. It's not meant for floors so much but I can guide you if you want to get fancy and really make those floors pop.

I think the main thing is to not make any splinters. If you see that happening, stop and reassess.

Tools needed:

Large bucket with ringer attachment preferably on casters
Cotton floor mop and handle
Some kind of towels or other absorbent cloth.
Commercial buffer with scrubbing and polishing brushes (they have a felt pad too, but you can forgo that).
Floor wax

You'll probably want to wax it at least 2wice over 2 days. You can walk on it at any time.