hey welcome to MF!! i also went through this a few months ago.
yeah most legit shops wont touch the cats, but what you could do is look into a exhaust system with high-flow cats, its a bit more but sounds a lot meatier.
otherwise if u remove a cat its most likely going to throw a check engine light. but with highflow cats u can still pass emissions and get a decent noise.
idk if this was a fluke, but i had a 2003 mustang v6 and all i had done to it was a catback flow masters exhaust sytem, and it sounded good, i mean Really good. so basically i had the stock 4 cats but not only did it sound very loud, it had a nice deep rumble to it too.
right now you got just the muffler so im guessing thats prolly why it sounds stock. but if you get the whole catback flow masters, or the catted high flow cat flowmasters exhaust system, it would sound much better. check out youtube for how other v6 stangs sound.