If you are going to target the brakes it sounds to me like the pins that retain the calipers are dry, as well as the ridge that the caliper rides on being dry. Due to brake heat the grease doesn't last long, and the surface gets rough and rusty. Try removing the calipers and wire brush all of the contact points where the calipers touch the caliper adapters, and regrese. It could also be a worn caliper piston or caliper that is not releasing fully, but the water lubricates things enough to make it act better.