Any viable X+L=J theory will need to explain not only why the Kingsguard were at the Tower of Joy, but also why it was so important to Ned to protect the secret parentage of Jon Snow.

This is hard to do, which is why I think most people accept R+L=J and discount the fact that Jon doesn't have Targaryen traits.  They point to things like Baratheon hair being dominant in Cersei and Jaime's children, and so maybe Stark traits dominate Targaryen traits.

So it is a real challenge, and maybe it is a dead-end, but surely worth considering.