That would be the first thing I would replace.
It is probably due to the "no cat". Those computer controlled motors need stuff like that on them, for 1 thing it creates back pressure in the exhaust system which allows the rest of the system to work like it should. It might run great for a few weeks or even a few months, but somewhere down the road, it will require service because of the parts that were taken off of it. I personally am not a fan of a "cat", but if it makes the motor run correctly? Taking off the cat, and changing out the muffler to a glass pack or similar style like a flow master, just adds problems.
'87 YJ, 4.2L built and bored, 8" of lift, 8.8 rear, AX15/NP 231J, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...