I'm trying not to let the perfect be the enemy of the good, so I'm calling the closet floors done.
The striped effect is from the different ways the floor was formerly finished. From the left, previously unfinished, paint on bare wood (you can barely tell the difference in the first two), and paint on primer. I doubt any amount of sanding would have evened out 80 years of different absorption rates, but wood conditioner may have made the difference less noticeable. I used three coats of Zinsser SealCoat to finish them. It is a de-waxed shellac. There are plenty of websites that outline the pros and cons of shellac, so I won't go into that here. I'll just say that it's often a better fit for old homes than polyurethane. I sanded lightly between coats 2 and 3, then buffed with 0000 steel wool after the third. The result is a lustrous, smooth finish. Not smooth enough for a Risky Business reenactment, but smooth enough.
Unintended consequence: I can now make good on any promises to give somebody a good shellacking. Or a mediocre shellacking at the very least.