Three thoughts. First, I had a similar problem on my 97 RT. It turne dout to be a relay that had worked itself loose. After shotgunning about $500 worth of parts it was fixed by pressing my thumb on the relay to reseat it. Expensive lesson.
Second thought. HES. If you haven't replaced it, it's time. You don't have a classic HES failure, but it's close enough.
Third, your O2 sensor. I had a similar problem with my GS. IT was rleated to the O2 sensor. Pull the cat code plug in the fusebos and see if that fixes it. On your bike pulling the CCP disconnects the O2 sensor.