Interesting dilemma. You already know that your horse can get footy in wet conditions, so that would put a monkey wrench into the equation. As someone who's horse decided to shed his soles a week before a show and made himself ouchy, I know where you are coming from there. The wet conditions = ouchy horse has me caught in the same dilemma.
If shoes do make your horse prone to white line disease, full time wear might not be a good option. What about splitting the difference? Shoe him with rim pads to help diffuse the peripheral loading factor and let him go barefoot on the off season to allow his feet to recover? If your farrier does shoe him, just make darn sure those frogs still come into contact with the ground upon loading the foot, or else that foot will start to contract again.
You just have to see your distance...you don't have to like it.