A rudder is probably not a good idea for surfing. First, it will be out of the water a lot of the time. Second, it is prone to breakage.

I suspect that you're correct about the Cheasapeake 17 not being ideal for surfing. I don't use my Cape Charles for surfing either. (I drag out my FG Pintail) The Cape Charles also tends to bury its bow. I think this is a result of a narrow bow and a flat deck that doesn't shed water fast enough. I think the bow shape of the Cheasapeake 17 is similar

The surf zone can be dangerous. Your best bet is to go out with a group of experienced paddlers. They can offer advice and an added margin of safety.