Funky cathedral ceiling with flat root

I have a flat root house built in ’62 with steep sloping roof pitches off the sides of the house. The upstairs gets incredibly hot and when I look in the “attic” space it doesn’t appear to be adequately insulated. (Checkout the image to see the detailed view). I’m thinking of installing a foam board insulation or batts in the rafters, but I’m worried about not having adequate ventilation against the rafters then. There’s no ridge vent for me to install venting to, just about 4 smaller soffit vents. Should I just install a radiated insulation barrier? How could I better vent this space?

(San Francisco Bay Area)

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