How can I cover up wood floor stain spill damage?
When using Oxalic acid, which usually comes in a dry crystal form, mix it with hot water, as hot as you dare, reading the labels for mix ratios. I mix it a bit stronger than they say, but that is me, I do stuff like that. You are new to this I don't recommend you do that, stick to the directions.
While the mix is hot, pour it on the floor the same way the stuff that stained the floor did. Let it set as long as it takes to get into the same places as the fluid did that did the damage. According to the end grain discoloration, it was wet for a long while.

Keep it wet, keep the mix hot if you can, the hotter it is, the easier it works, the faster it will soak into the wood end grain. Do not let it dry out over the time while you are working with it, keep it wet.

If you went really overboard with the acid, I don't think you would ruin the flooring. Yes it will swell a bit, but it will dry back out. Any small gaps created by the flooring swell, will far less noticeable than the gray streaks the stain has.
The trick about keeping it wet is, when oxalic acid dries it forms at the least a white haze. Not dry=no haze. If it does haze add more acid, a simple fix. The important thing is the cleanup. Have a clean 5 gal. bucket of water, a scrub brush and plenty of towels. Use the brush with plenty of water, drying it up with the towels. Do this 3 or more times, 5 is not out of the question, cleaning MUST be thorough. I had done this on wood walls with a hose and brush with constant running water and still had haze here and there.

Let the floor dry out for a couple of weeks before trying to repair the finish.