My replacement Betz board seems to need the reset line (my first one didn't).

So I'm going to try to implement it. Can you explain more about your reasoning for your code for the pullup/pulldown code?

At startup, your code did:

pinMode(51, INPUT_PULLUP);

Then delayed for 300ms then did:

digitalWrite(51, LOW);
pinMode(51, OUTPUT);
digitalWrite(51, LOW);

Then delayed for another 50ms then did:

pinMode(51, INPUT);

My questions are:
Should the default state of pin 51 be "INPUT" most of the time?
Why the "INPUT_PULLUP" at first then?
And why the 300ms delay after the INPUT_PULLUP?