What do you expect the Styrofoam peanuts to do???? They're soft, gentle and meant to protect things. Do you expect them to scrape the walls of the tank and clean it - trust me, they won't.
And then they're going to clog up the leach field in some campgrounds septic system. If you're going dump them into a municipal sewer system, they aren't going to like it either.
Use the dish soap if you want, but don't use the peanuts!!!!
Bill
Nodwell RN110 out moose hunting. 4-53 Detroit, Clark 5 spd, 40" wide tracks, 10:00x20 tires, 16,000# capacity, 22,000# weight. You know the mud is getting deep when it's coming in the doors.