Right, I did make one further discovery this past weekend, which was that my assumption that IR7 was vsync was wrong: IR7 is actually the only interrupt that's always disabled, and IR0 (pin 18, as you observe) is the only one that currently makes the machine move forward. Except all that happens is it fills the screen with the character "6" and glitches out heavily in an infinite loop.
Pins 20-24 being connected to a 74LS14 means those interrupt lines probably need to be inverted due to the chips involved supplying their own interrupts with inverted polarity.
74LS14 is a hex inverter. The output pins are 2,4,6,8,10,12. So some combination of 5 of those pins would be what are connected to 20..24 on the 8259.
The corresponding input pins on the 74LS14 are 1,3,5,9,11,13. Which of the pins on the 74LS14 go to pins 20..24 on the 8259? And what chips feed the corresponding inputs on the 74LS14?
Are you sure that it's pin 4
of U45 that is connected to the I8259 pin 19? Pin 4 on the Am9513 is an input pin, so that doesn't make sense. Are you sure you don't mean pin 37 on the Am9513, which is on the opposite side, but is an output?