On Friday night, I emailed both FLExLight and Sharp, asking for the datasheet for the LS018B7DH02. I honestly wasn't expecting to get a response, but (as briefly mentioned in my last post), Adnan and Yulia from FLEx responded Monday evening. Tuesday morning, both they and Beth from Sharp responded with a copy of the datasheet! Half of it is in Chinese Japanese but the important parts:

The third image is something I wouldn't have noticed if Adnan from FLEx pointed it out to me: there are 240 clocks for each line, but only 230 horizontal pixels. This means there are 10 dummy "pixels" for each line. The datasheet says that they don't matter, but that they're recommended to be zeroes. 

I've ordered a replacement display, which will hopefully be here by the weekend. More updates once it's here and I can get it working.