Andy, I have thought about just dropping everything and doing the WOD for my training, but it intimidates me. For one, I just don't yet have enough faith to put my training (which is so important to me) into the hands of someone else, where I don't even know what is coming from one day to the next. I've finally started making good progress with my running by committing long term to a comprehensive training plan, and I recently decided to do the same sort of thing with my lifting (doing OLAD). The truth is, in the past my training was much more like WOD, doing some lifting, some bodyweight stuff, some track workouts, some distance, etc. sort of randomly.
Also, getting started with the WOD is intimidating because I would have to start from scratch learning a lot of the more technical O-lifts (I like power-cleans but I've only dabbled with squat-cleans and snatches and the like) and gymnastics stuff. I don't feel like I have the time for such things right now even though I'm sure it would benefit me over the long term. But at the moment, I'm training to be an Army officer and I'm taking PT tests every six weeks.
But I am willing to experiment with the kipping if you really think it will help. I can take those Saturdays that I planned on testing my max and instead do some ladders or something with kipping.