Most of the online recommendations were to change the filter and check the supply pressure. Those were both fine, so I figured it had to be the water intake valve. My LG fridge has two water intake valves, and there was no easy way to determine which one could be the culprit, so I bought both. After watching the video, I replaced the primary valve in about 10 minutes which fixed the slow water problem, but it was still leaking. So I watched the other video and replaced the second intake valve, and that fixed the leaking!
The videos were great and the repair was simple as a result!