Here's how I would have done it if I'd been writing the Tower of Joy. Aside from better fight choreography and no dual wielding, Dayne would survive the fight, although Howland would still save Ned's life, making that part of the story true. Ned goes up into the tower, scene ends. Then, at the end of the episode, Ned comes down out of the tower, sun is close to setting (so you plebs know that time has passed) and he just walks right up and murders Dayne in cold blood.
I think it would be shocking enough to suggest that perhaps something more complex than Jon being the son of Lyanna and Rhaegar, and make people start wondering. But it is as simple as R+L=J, Ned just snaps when he realizes that his father and brother were burned alive and the country went through a civil war simply because his kid sister eloped with a prince.