I would rather have the boat tow "bow high" than worry about water coming over the bow. Honestly, I really don't see any issue with the bow riding high.
And, depending on the brand of boat, I would be very leery of using the cleats on the boat. Last year we were in Bullfrog, and a big windstorm blew through. There was a Bayliner tied to the dock that the cleat was pulled off during the storm. The bow and stern eyes are reinforced enough to be able to use as lifting points for the boats.
And I think it is a good idea to use floating line. But I have been using cotton anchor rope for years. I'd hate to get it caught in the prop, but if you are cautious, I think the risk is low (hope I didn't just jinx myself). I think there is more risk of sucking a rope into the prop when anchoring the boat than towing.