The only time I've really had an experience with this was after a few months of daily (or near-daily) use. I started to get the kava dermopathy and decided to stop.
That day, I made food in my kitchen, giving no thought to the bags of kava next to my granola. Of course, I wished that I had some for my troubles sleeping and anxiety (for which is the primary reason I use kava), but I had no cravings. There was no withdrawal, no craving and no obtrusive/repetitive thoughts about kava.
I wholeheartedly believe that kava is not addictive. In fact, it has been shown to have
anti-craving effects.
Sure, you can gain a psychological dependence on it (as in, depending on it to help you sleep), but we all develop psychological dependencies on countless things we all take for granted in our daily lives. Television, cell phones, internet, transportation, human interaction, money, etc. Take away any of those things and I'm betting, you will have a much more difficult time than taking away kava.
I too am in recovery, and I would have to go out on a limb and say that if you can't stop even when you want, the kava is using you. The old adage of "I didn't want to use, but I did" that shows some sort of addiction... I would be concerned with that, although I've never had that experience.
Just my 2 cents