I might have found a simple, free fix for this problem:
I have a 2 year old LG DLEX8000W that suffered from the same problem of drum turning whenever the door was shut. It's stacked with about 10 inches of clearance to the ceiling, so I really didn't want to attempt a disassemble. I had tried cutting the power to it at the breaker without success. I had been putting up with the problem by leaving the door open between runs, but sometimes it ran run for hours when I didn't hear the beep after the end of a cycle. I estimate I did about 15 loads with the malfunctioning dryer over the course of 1.5 weeks.
Recently I wanted to dry a load of dress shirts for which I had created a custom cycle of the lowest heat for 20 minutes followed by the "wrinkle care" setting, which turns the drum on every couple of minutes to agitate clothing to prevent wrinkles for forming before emptying. I'm skeptical that this setting does much for wrinkles, but I think it solved my problem because after my custom cycle, I was surprised that the dryer stopped like it should. I've now done about 5 loads, and it appears to be back to normal. I'm not an electrical engineer, so I could only guess why this worked for me. Perhaps the "wrinkle care" setting drives the relay a little differently. Or perhaps it isn't the wrinkle care setting but rather something related to my custom program or just a random coincidence.
I'd like to hear if this fixes the problem for anyone else. Was it a fluke for me or is this an actual fix?