The bulb convertor on that first Pilot pen just wasn't cutting it, so I ordered a piston convertor. While I was at it, I went ahead and threw in another Pilot and conveyor. The notebook was just an easy way to bring the total up to free shipping level, but I actually like it. A lot. The Apicas are turning into my favorite line of notebooks.
Okay, so user error may have been the major cause here. Turns out I wasn't pumping the squeeze convertor enough. You're meant to pump it until bubbles no longer form in the ink, then let it slowly draw until full. Previously, I wasn't seeing bubbles at all because I was compressing the bulb BEFORE I submerged the nib, and only letting it draw once. It's possible that what little writing I got out of it each time was just the ink in the nib. I've filled it properly now, so we'll see how it goes.