Would adding 9" of insulation for $1600 provide a significant energy savings payback in a hot desert climate? Is this a project that should only be done by a licensed, bonded and insured contractor for liability reasons?

but..sealing the openings from attic to
living space below should be done first.

hvac supply boxes where they penetrate the
attic floor,
cuts around bath fans, oversized
cut for stove vent and recessed lights.

all these openings allow attic air & insulation
particles to enter your home.
in sealing these areas you improve the air barrier
at the attic floor.

you would use mastic tape to seal the hvac supply
boxes..from inside remove supply grill. use tape
to seal sheetrock ceiling to the inside of the supply box's
metal lip.
hopefully your hvac company mastic sealed the ductwork,
but take a look and see. most do not address the
sealing of the supply boxes to attic floor.

most existing homes have duct leakage of about 30%.
air that you pay to heat and cool that never makes it
into the house.

recessed cans..ice chest method in attic or air tight insert from inside. get brand name & model number to
shop online for air tight inserts.

bath fans cuts can be big..I use the mastic tape here also.
sometimes the stove vent can be sealed with caulk..but
mastic tape may be used here also.

I use hardcast brand mastic tape, from hvac supply.
mastic sealing the ductwork (esp in the attic)
is also a good savings. you can use a paint on mastic
that is applied with a brush. duct takeoffs @ supply
plenum are usually big leakage areas.

keep in mind that cellulose is ground newspaper.
it creates a fine dust that enters thru all the cracks
in the attic. thus the reasons for improving the air
barrier.
insulation doesn't work when air is moving through it.

you will see a savings & improved comfort in adding
insulation. more so if you do the work above prior to
insulating.

I don't understand why the need for closing off the
soffits..can you explain a little better?
do you have ridge vent & soffits?
in an vented attic there needs to be a way for
cool air to enter (soffits) and exit (ridge vent).
also you should install baffels to keep insulation
out of soffits and provide a pathway for air.
can you describe the type of ventilation you have?
soffit.ridge vent
gable end
soffit & passive vents (whirly birds that may just be a La description)

I can't imagine life without high humidity!
it is a killer in my hot humid climate.
makes for some long hot hot summers.

best of luck

there are several posts in hvac forum
about insulation. give them a read.

best of luck.