2.3" 16 segment common anode LEDs, HT16K33 and ULN2803 (now common cathode)

MitchSF:
That's why I originally put 5v on VCC for the Max626.

That does not work when the MOSFET is powered from 12V.

MitchSF:
I thought the pullup resistor was only necessary when the 74HC04 was used.

The HT16K33 output is a pulldown output, it always needs something to pull it up.

MitchSF:
I'm not sure where to go from here.

Find another mosfet that can take 20V over Gate Source, you do not need a logic level one.