The old roof hip is a 2x6, but today has to be one size larger than the commons. 24"o.c., IRC says 2x6 will span- 11'9" only, with no snow load. So it should be 2x8= 14'10" span. Plus it has to hold the new over-frame and ridge of new. I would build it to the second choice for certain.Leave the old ceiling joists. Be safe, G