There are 2x rows of small radial caps at the back of the LCD panel that need to be replaced.
Here's a picture of my disassembled LCD. The 2x4 row of black things are the radial caps. They seem to be 3.3uF 35V as best I can tell. Thanks for pointing those out, I didn't find them in my previous attempts. There are two radial caps on the center controller board, and that's all I could find. All the replacement radial caps I can find for those are too tall to reinstall the front bezel, so if anyone knows a replacement part for that, I'd appreciate knowing what it is. There's none on the brightness/contrast board or the cabling board.