After much testing and thinking, I've (finally!) found the issue in my project preventing BASIC from running properly.

After the test program worked, I reflashed BASIC to the EEPROM and started the SBC with it. To my surprise, it booted just fine, and BASIC worked as expected. However, when I clicked the reset button on the board to test if it would work a second time, nothing happened. I kept pressing it, and after about 10 tries, it finally reset properly. Strange. The last thing that I would have expected to have caused all of the issues I faced was a faulty push button. So, as confirmation, I attempted to reset the board by shorting the reset pin to GND, and it reset immediately every time I did it. Well, that explains it.

Next up, I'm going to work on a way to test the CTC and do some basic timing operations.