Is your car auto or manual?
I have a similar system on my ED XR6, with the cat moved under the car, it is a 3" cat. Its been on there for five years, new cat last year, NO cat prior to that(i lived in the Territory were it was sort of legal to have no cat). I have never had a problemwith the system as it was.The only problem was an O2 sensor that shit it self(with similar symtoms to what you have described) put in a new O2 sensor and all was great.
Hope it helps.