Thanks again for your advice! We ultimately gave the floor a second coat and we also switched to a darker stain - the first coat was pecan, and the second coat is walnut. The darker stain covered the uneven patches and the swirls nicely. It's a polystain so we're finished in that room now, I think. It's not professional quality, obviously, but it's much better than it was, and plus we learned a lot in the process. I'm going to try uploading a picture.