In the past, I have used an epoxy-type produce, made by Permatex, I think,
which can be used to restore stripped threads. You spray the male thread
with a release agent, and then smear on the plastic. Then you insert the
screw in the hold and let it cure. Then simply unscrew the thread from the
now plastic threads. It is not recommended for applications with high
stress or vibration, but I am sure it would work fine on drawer pulls.

You could either drill out the old 24 pitch threads, or force assemble with
the 8-32, using the resin for reinforcement. I would be inclined to
partially drill it out, leaving enough of the 24-pitch thread to help the
bond, while still permitting a cross-threaded assembly without too much
hassle.