Alas, I've wiggled it around every which way and pulled it out to where it just hits the lock plastic chip and then turned on the system, but the result never changes. I cleaned the system contacts a bit by putting some alcohol on the end of the Arcade Card, but again, same result.
Since my only other HuCARD is an Everdrive, I am wondering if its added thickness pushes it closer to the contacts in the system and thus makes it work every time I insert it. I wish I had another game card here to verify this theory. What's interesting is that Sapphire boots, meaning that the system reads the card, though not well enough to use its memory after the game boots. I'm assuming that the system checks for contact on, say, one of the pins of the card to verify that the card is in the slot, but uses all the pins when a game is playing — and once the game boots, it fails to access the card through these other pins, causing the glitching graphics. Or it's possible that all the pins are making contact, but the Arcade Card itself is fried.
I'll check out my local hobby stores this weekend for some scrubbing equipment and also open up the system to see what the contacts look like on the inside.