Cody: Most old hats are not 1/8" thick. they are much thinner. Felt does weigh more than styrofoam, which is why we are all experimenting with the stuff. Styrofoam also will not absorb lube, adding to its weight, and making it travel further out the barrel than if it is dry. Being dry, the styrofoam separates from the shot very quickly, and floats to the ground, often taking the overpowder card with it. You rfelt hat, even if you find one that is 1/8" thick, will weigh much more than the styrofoam, and if you soak it in lube, or fub lube on it before loading, it will carry that lube with it out the barrel and not separate from the shot as quickly as the styrofoam does.
The serious ML shotgun shooters I have met have gone to Styrofoam for a reason, and you can see it in how well their guns pattern and break clay targets. Because stryofoam is so light, it makes a quick reload, as they pour powder down the barrel, then put a card wad and the styrofoam cushion wad, and push it down the barrel with their finger, then pour in the shot, and then place an overshot card in the barrel, and run the entire load down the barrel with one stroke. The process saves them both time and energy for shooting long matches, and they come prepared to shoot a hundred to 200 shots in a day! They use dippers for the powder charge and the shot, and their range boxes carry both the powder, shot, wads, and cleaning patches, in set locations so that they limit their hand motions and conserve energy even doing this.