I'm not there and so can't see exactly what you're up
against, but here are a few observations:

You know you can take the whole housing off very easily, and
then maybe drill the old screw out, right? Then if the
female-side threads are toast, you can drill a hole through
the next rotor and all the way through the distributor's
shaft. Affix the rotor to the shaft with a cotter pin. I
used this fix from 2002-early 2003 when my 1991 Civic's
(allen wrench socket) rotor set screw threads etc. stripped
and wouldn't hold no way no how. 2002-2003 was a painful
year of going back and forth to the shop, since the bozos at
the dealer didn't know how to deal with this, and I wasn't
savvy then.

Another guy here used the cotter pin fix for years.

In 2003, I ultimately had an arguably overzealous,
money-grubbing independent honda shop declare my cotter pin
fix unsatisfactory and declare it was behind my intermittent
stall problems. (Wrong! Ten days later I'm back and, with
some nudging from me, they admit it was the coil all along.)
For the first visit, they replaced the whole housing on my
91 Civic. After this, I got really savvy (well, relatively)
on Honda distributors. Now I replace my own igniters, coils,
housings, etc.

In hindsight, given that my igniter's electrical harness was
falling apart in some places, and that a new housing
includes a new harness, plus a new bearing (which are also
notorious for failing), etc. I am at the point where, as I
said before, I advocate a new distributor housing about
mid-life of 1990s Hondas.

A fellow posted in 2005 with distributor problems and took
himself to Autozone and got not just the housing, but the
housing with coil and igniter for IIRC under $200. (Whereas
Majestic would want the $250 + around $80 for the coil and
another $80 or so for the igniter.) We cautioned him not to
bet that this would last more than a year or so. He said if
he got a year out of it, he'd be happy. So it was a rational
decision.

As for my new distributor housing: Babe my 1991 Civic hasn't
seen the inside of a shop for three years now. No
breakdowns, either. At 175k miles, she purrs.  I carry an
old, but working, spare igniter in my car.  Had the housing
off a few times now to clean up underneath it. :-)

I don't think you need to do that.

Remove the distributor from the car. That's easy and then screw removal is
a lot easier.

Have you stripped the Philips cross? If not, the use of a drill press as a
screwdriver-bit holder may help.

as recommended by others, remove the distributor.  before doing so, mark
the casing relative to the head assembly so you preserve the timing on
reassembly!

then, if you have an electric drill/driver, use a NEW bit to unscrew the
screw while applying good axial pressure so it doesn't strip.  if you're
doing it by hand, again, tool quality is paramount.  cheap phillips
drivers are guaranteed to strip.

i'm not sure if lubes will ease the thread in this case - it's got a
loctite compound on it.  if worst comes to the worst, smash the old
rotor off so you can get at the screw head with small vice-grips.
guaranteed to work.