This time I did all three rounds of sanding and polishing. The pumice did make quite a difference, and I will be using it again for the remaining coats.
The only frustration was finding quite a few dog hairs in the finish. I wasn't able to remove them, so I will have to rub them out. I later found that my shop coat was covered in hair. I will make sure in future to use a clean coat when working with the varnish.