If the truck has non-stock exhaust it probably has a non-stock intake as well, and that drone you're hearing could be coming from the intake side. I had a '95 F350 for almost 15 years and did many mods to it, one of them a Tymar intake. The amount of noise from under the hood definitely increased when I replaced the stock air filter box with the round Donaldson filter.
But, it also had a 4" turbo-back MBRP exhaust that while it included a muffler, it was also louder than OEM. In my opinion, lowering the cab noise in any of the 7.3 trucks is going to take more than just adding a muffler.
:):)