Has anybody done this?
So you want to know if you could run one "dummy" cat (being gutted) and one regular one? If you did, I'd buy a high-flow one. I know you don't want to spend the money, but otherwise you'll just be clogging up half of your exhaust. The side with the gutted cat will be flowing quickly and smoothly while the other side is trying to fight through a restrictive cat. If you choose to add a working cat, make it a high flow one, otherwise you'll just be hurting your power output. There's a reason they make high-flow cats: for the people that have headers and need that free-flowing exhaust. The stock cats (or the ones like them) do not flow near well enough for headers.
The only other suggestion for getting rid of the rasp is to change catbacks. Most people who have LoudMouth with LTs end up changing the Loudmouth later on down the road.

