I had something similar happen right after installation of my SC, same codes too. Replacing O2 sensors seemed to help, but didnít. Solution was replacing the spark plugs with a narrow gap NGK and itís been great since. Hope you get it sorted out.
Well, I now see that I had two separate problems.
The post-heat-soak bucking that I was experiencing and the P0339 code were definitly due to a bad crank position sensor. That thing not only pokes into the crank case and comes into contact with hot engine oil, it is between the catalytic converter and the block on the passenger side so that little sensor sees some heat. I replaced the sensor last Thursday and then drove to the Rubicon, through it and back in the heat and not a single issue.
In fact the sensor has been causing me grief for a long time, i can now verify. I've been getting very mild hesitations in the mid range and near redline. I was also getting an occasional cut out when accelerating hard under load where it would buck hard and then keep climbing the RPMs. Never any coded and now all those issues are gone.
I would also say that it runs a little better at super low RPMs out on the rocks. I have a much better stall point now than I did before. I noticed it immediately on the Rubicon because I could now run into a lower RPM when crawling before stalling the motor. It works a LOT better now at the super low RPMs. I had to relearn my stallpoint at first. I still manage to stall the motor from time to time though with my manual transmission.
Replacing the o2 sensors also gave me something. It runs a lot smoother from that as well. Even through there were no identifiable leaks at the sensors, I am getting a lot less popping and crackling in the exhaust on decel.
It actually runs better than ever now - very responsive and does not skip a beat from idle to redline even through it is still throwing the P2098 and P0430 codes. I hit those codes this weekend on the Rubicon but without issue. Cleared them and hit them again on the freeway drive home. Again, it was running perfectly and the light just came on.
Ignition coils are new and the plugs are not super old.
I'll keep poking around until I get P2098 and P0430 nailed. Runs perfectly otherwise.