Craig,
If your bird wasn't pressurized I don't think I'd want to take on replacing
the window.
But....
My windshield cracked in transit from Redmond to Colorado in the back of my
Ryder truck. Of course, the top of the fuselage was still off the airplane
and the layups weren't in place around the window either.
I was able to remove the windshield with a small pry bar in about 5
minutes. The Hysol stayed stuck to the fiberglass and made a nice release
for the new windshield. You are in luck because you can remove your door and
don't have to work inside the fuselage.
I would carefully cut the layups around the edge of the Plexiglas and use a
pry bar. Who cares what happens to the window! You could sand down
the layups or leave them there. If you could get the new window to fit
tightly without drilling all the holes to secure it you might be able to save
the paint. Maybe just weight to hold it tight during bonding. You
will likely need to touch up the paint, but even that's easier on the door than
the fuselage.
If you resign yourself to repainting the door, I would use a heat gun to
remove the layups and drill the holes to hold the window during bonding.
Mike
P.S. I would guess you got some chemical soaking into the Plexiglas
during the paint process.