Adding insulation above a vaulted ceiling?

I’ve got a 1955 house with some definite lack of insulation.

Many of the ceilings are vaulted, but I can access the end of the joists in the attic. Problem is there is about 4-6” of clearance between the back side of the ceiling and the roof line.

Any idea how I would go about adding insulation here? Is this “hire a professional” territory? I’ve blow insulation into a normal attic, but have never tried to get something over a vaulted ceiling.