As I was reading through this thread I was thinking the ECM reset was a good starting point. So you get
I've also noticed that it wasn't mentioned before. Once the battery was changed after the AC issue the engine gremlins seemed to be a side effect.
Disconnect the battery and cycle the key to start once to do a full system drain and hook it back up and take it for a ride.
The problem with a "fuel system flush" is that if there is debris in the line, it gets pushed to the injectors if they're not pressure cleaned. You can unhook the injector rail and empty it. (pull the battery cable or pump fuse) Get the truck up to operating temperature, then pull the rail as stated above. Pull the shrader valve from the fuel rail and fill it with sea-foam. Re-install the valve and fire it up while it's still warm.
That's the backyard way to get as much concentrated cleaner under pressure to the injectors. You can also buy a test noid to check them for pulse.
I further question the removing the exhaust and releasing the back pressure to start it. It seems odd and causes me to consider if the Cat that was installed has sufficient flow. Even a new Cat expands under high temperature. If it's too small the truck can't pull air in if it can't push the exhasut out.