First we called for "professional" help. Those guys took $60 of our money and said, "Get a new one, it'll be cheaper than having us fix it."
Then I found this site and videos and saw that other people had the same problem I had, common for LG washers after about 7 years, when the bearings fail. If I could replace just the bearings, it would be cheap: your site had the new bearings for around $65. But I saw another user recommended getting a new rear outer tub assembly to save time and the hassle of knocking out the old seals since that could be problematic. So I did, since the $200 part was still better than buying a new washer.
The videos are great. My recommendation: watch several of them for the same or related repairs because the different techs had different useful tricks for disassembling and reassembling the washer. On the way to replacing the rear outer tub though, I found I could not separate the old inner tub from the rear outer tub. Years of rust had built up and even using a rubber mallet or the trick the videos showed of putting a board over the end of the spider rod and hammering it out did not work. I could have used more force but worried about damaging the inner tub or spider.
So I bought a new inner tub assembly and it arrived a few days later. The seal I ordered fit right into the groove of the new rear outer tub assembly just like the video showed, and the new tub slipped right into place too. I continued to follow the instructions on the video and reassembled the outer tub and then reinstalled it in the washer housing, reconnecting various tubes, shocks, and wires as I went. That did the job and now the washer is quiet again!
The whole job wasn't that difficult but is a tedious process and there are a lot of steps. I only needed help from someone else once, and that was to lift up the tub so I could reattach the suspending springs to the sides of the washer. In the video the tech named Simon shows how you can use string to lift the spring to the washer wall, so maybe I could have done it completely on my own.
In the end, was it worth it? I think so. The total cost, including the fee the "professionals" took in exchange for nothing (though I get it: they can't come out for free and at their labor rates it really would have been cheaper to buy a new washer) the total cost was about $480. That is more expensive than a new $400 top-loading washer (that wouldn't have matched the current dryer), but still cheaper than a new $750 front-loader with comparable features. Better yet was the satisfaction of not succumbing to "disposable society" syndrome and maybe now getting another 5-8 years out of this washer.
If you have this problem and can spare the washer for a week, take it apart first and see if you can separate the inner tub from the rear outer tub before ordering your parts. If you can, and are able to remove the old seals and bearings, then you can reuse your inner tub (and spider, if undamaged) and do this job for a lot less money.
Thanks to AppliancePartsPros.com for the great help, videos, parts, quick shipping, and even the other user stories. I couldn't have done it without your help.