Overframing hip roof?

I've got your basic rectangle shaped house (40'x 27') with a hip roof. Roof framing is all 2x6. I'm adding on a large addition to the 27' wide end that will make the house essentially L shaped. The new addition roof is higher than the existing roof so I need continue the existing house ridgeline so that it "dives" into the new roof.

A few folks have told me to leave the existing hip roof structure and just overframe the existing roof. The existing roof framing is all sound. The other alternative is to completely remove the hip and jack rafters on that end (basically the last 14 feet of the roof) and just replace with common rafters that match the existing common rafters.

If you were doing this which way would you go.