There is no effective insulation in your home.
There are various ways you can solve the
problem, each has a cost, but doing the job
properly will make your home much nicer to
live in and it will be a lot cheaper to run.
How long do you intend to live there?
The most effective way to insulate your
home from the sun, it to take the roof off
and cover the rafters with a sandwich of
oriented board and polystyrene and then
put the roof back on.
(You need at least 5 inches of polystyrene
in the sandwich....8 inches is better)
This system is called SIP's.
Done properly this isolates your home from
the effects of the sun. The oriented board
sandwich is fixed to avoid any heat bridges.
Most of the heat gets into your home by
conduction, some by radiation and some by
Repeat the system over the walls and you
have one cool home.
This solution is the best you can get and
really the only way to keep your vaulted
ceilings looking great and keeping you cool.
Take a look at the duct work, is it insulated
and air tight?
The fact that it works at all in the heat is
some kind of miracle. It needs at least 4
inches of sprayed foam covering all sides,
again 8 inches will do a better job.
If the above proposal is too expensive, then
fitting sheets of polystyrene cut to size
between the rafters and below the rafters
will provide a great improvement. Use one
inch and two inch thick sheets, cut them
with a knife to a push tight fit.
After doing the roof, fill the spaces between
the joists in the same way. For the best
result pull the ceilings down and fit three
inches of polystyrene sheet across the
ceilings below the joists to stop the
conducted heat coming through the joists
into the rooms.
This system will spoil the look of your
vaulted ceiling but, you can create another
fake ceiling below your existing one.
Then use the same system in the outside
Cellulose and fiberglass are rubbish and
cannot keep out the heat, they are both
conductors of heat, remove the so called
insulation you have and dump it.