I got my skimmer and return in today as well, and now I'm continuing to fill the rest of the pool. I only need about 6" of water to be at operating level, but I also need to backwash the filter before its first use, so if I go over the level I don't mind too much.

I added a few cups of bleach this evening and stirred the pool with the strainer again, so hopefully that will help a bit. I'll check the level in a few hours to see how it looks. Regardless, I'll be circulating water tomorrow afternoon at the latest, and swimming the day after that if all goes well.