I HAVE THE ANSWER!!! I have the same machine, same age, same symptoms. Mine started acting up in February. After three visits by my repair person and a lot of research on his part it turned out that the Vibration Sensor needed replacing. It communicates between the brain and the hall effect sensor if the machine is out of balance or not. In my case, it would say it was out of balance when it was not, and that it was in balance when it was not, preventing the machine from rebalancing itself. When he ran a report the readings were showing the machine was out of balance when it wasn't even operating. That was the big clue.
My repair person said that he has not seen other similar machines that use this sensor. I shared with him your problem and all the advice given and he said those were right on with normal logic. The problem, this particular model is just slightly different.
The part is called a Vibration Sensor (though you might see it called a humidity sensor).
The LG part number is EBD48922801.
My repair person charged me $89 for the part plus some labor. I'm ecstatic after fearing I would be replacing my $1400 machine after only three years. I know its bittersweet since you already spent a lot.
I may need to replace my shocks as they got stretch a bit with all the out of balance episodes while we figured it out, so look out for that too.
Oh the joy of fresh clean towels!! It's been too long!!!