Sliding glass door , no room for header ???

[Ginofav1]

Hello all , I am looking to install a 6ft sliding glass door in my single level ranch house . I am running into the problem of installing a header . I have low ceilings and not enough room under double 2x4 top plate to install a header . I have an interesting construction at the house . There is a double top plate with ceiling joist on top of that , then I have a triple 2x4 plate with rafters on top of that . I was thinking I could cut the double top plate and put a 9inch laminate beam for my header . Suggestions??