I would suggest to avoid adding supporting edges when you start modelling an object since it hinders in visualising the primary form of the object.
If you really want to visualise the mesh with subdiv, then add a bevel modifier with limit set to angle (30’ or adjust as per mesh) and later add extra edge loops when you are satisfied with primary form.
Also always keep the Mirror Modifier above other modifiers like subdiv to avoid any issues.
PS I have attached the modified file to give you an idea.
hob_mod.blend (633.4 KB)
Also take a look at look at EdgeFlow addon(absolutely free and awesome):
It will be helpful in getting the curvature you are trying to add to mesh.