A junior high school girl did a test of different toilet papers to see which one dissolved the quickest for her science project. The results were posted here a few years ago. She had several tests, one of which was placing the TP in a jar with water and shaking it for 30 seconds. As I remember double ply Angel Soft performed the best. It's what we use.
We used to use Costco Kirkland brand TP, but had problems with the pyramid of death forming in the tank just below the toilet. After changing to Angel Soft, we have had fewer issues. We also add liquid detergent and Calgon water softener after dumping and flushing to about 5 gallons of water in the black tank.