There was the tiniest solder bridge between pins 49 and 50 of the IT6613, shorting SDA to ground. With that removed, everything is working beautifully. I found that SDA was grounded while examining the LCD’s interface, but it was only through going to every possible point it was connected to that I found the bridge; it was such a tiny bit of solder that I easily missed it in my previous examinations, and even knowing what I was looking for, I could only make it out under exactly the right light!
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