In a cold climate, without an appropriate cover cloth, blown-in fiberglass can lose up to half its R Value. Consequently, I have only used blown cellulose in attics.

and in my hot humid climate...LOL!

you shouldn't have to remove existing insulation
to blow more on top. insulation doesn't go bad.

what you should do...in any climate..
is to air seal between house & attic @
ceiling/attic floor...before adding more insulation.
not only will this reduce air infiltration, but it will
improve both comfort & air quality.

check areas where ducts & bath fans opeings
in ceiling. by removing supply grill & bath fan
cover, you can see the oversized cut made in
sheetrock for install.
buy some Hardcast brand 1402 mastic tape,
use it to seal between sheetrock & supply box/housing.

I'll attach a pic of a supply box sealed this way.

recessed lights are a leakage sites...IC housing
has holes in housing & cut for recessed light in
the sheetrock ceiling has the same issue as above.
to seal these cuts...same thing...drop trim use mastic
tape..
you can address the leakage in housing by installing
air tight insert baffles. these also install from inside
the house.
or you can put a box over each one in the attic & caulk
it to the attic floor..box must have 4" clearance on sides
& top.

attic accesses are leaky.

once you stop the airflow through the insulation from
attic into the house, then the insulation performs at its
R-value. air moving through insulation not only robs the
insulation of R-value..but as it filters the air through the insulation
it brings into the house insulation particles, dust, attic temps
and here humidity.

address these issues first.
then..if you have ductwork in the attic...mastic seal it.

when all work in attic is done..then blow insulation.

hold off on insulation...until all your work is done.
otherwise you'll compress the insulation..and it will
be harder to see where your ceiling joists are...making
it easy to step wrong.

I'm not a fan of cellulose..but its a personal rather than
professional thing. while cellulose is a good product,
the ground newspaper produces a fine 'dust'.
this dust enters the house via the areas listed above
(and others)..I've had many homeowner complaints
about dust...then find out about asthma..allergies.
creating the air barrier at the ceiling attic floor is
very important.
and as briefly alluded to above..sealing ductwork etc.

its pretty rare to see 'itchy' blown fg. maybe in tract
housing..in my area.

just curious...what reason does roofing company
want to change insulation?
it doesn't make sense...to remove & replace insulation
unless it is wet.
this is kinda a red flag for me without more info.

and Worthy...
what kind of cloth is used on top of blown insulation
in your area? like the netting used for BIB's?

best of luck OP!

Thanks for the detailed response. I never thought about sealing the around the heating ducts and bathroom fans. I'll look for the Hardcast 1402 tape and do that before the job gets started. We are also having a few Solatubes installed at the same time so I'll make sure those ceiling fixtures are sealed.

I need to take out the old 4' fluorescent lights in the kitchen and replace them with recessed lights. I definitely need to do that before the insulation gets blown in. Isn't there suppose to be no insulation on top of recessed lights because of possible fire hazard?

We are the ones insisting on removing the old insulation. I have found some old evidence of rodent activity in the attic. That problem has been taken care of but I want to get the old stuff out before the new stuff goes in.

I have never seen any cloth put over insulation and the roofer didn't mention it. Maybe it's not needed in the San Jose, CA area? The temps do drop down into the 20's in winter and go over 100 in summer. Is it used to keep the insulation in place or is it used as a radiant barrier?

you'll have to get the hardcast 1402 at hvac supply
or online. it is great stuff that works & lasts like
no other tape I've used in my 15 years of
efficiency.
it may be that your hvac co can get it for you.
my cost is about $25 per roll with tax.

removal of insulation is a personal thing...
but with a good air barrier between rodent
activity insulation & living space below...it
isn't an issue...
here $1.00 per sq ft is removal charge..and
they don't do a good job, homeowner often
has to shop vac out feces & missed insulation.

when you replace the lights with recessed lights...
purchase ICAT. insulation contact air tight.
then you have only the cut in the ceiling to seal.

here is the pic I forgot to attach.
& radiant barriers on attic floor..gather dust &
lose reflectivity. the correct install is attached
to rafters with foil facing into the attic space.
the cloth would be used to keep the insulation
from blowing around..or that is what I think.

best of luck.