One final note...
I had been doing all of my testing on an x86 platform. Since moving the scripts/overlays to my RPI4, I had to increase the sleep outside the loop to 2 otherwise it wouldn't pause.
#! /bin/bash
while ! pgrep retroarch >/dev/null; do
:
sleep 1
done
sleep 2
echo -n "PAUSE_TOGGLE" | nc -u -w1 127.0.0.1 55355