I took the Golf back to the shop and left it. They gave me a loaner. A couple of hours later the service manager called, and said that the vibration was coming from a bad dual mass flywheel, that this was a known problem with this car, that it had nothing to do with the axle, and that since it's so expensive to fix I should probably just put up with the noise. He said that they could recreate the noise with the car out of gear (which I could not), so it was definitely the flywheel. He would give me a copy of the TSB, and I could research it and get a second opinion.
I've been going to this shop for over 17 years, and have never had any issues with them. They're not the cheapest shop in town, but they've always been fair and honest, and I never felt like I was being ripped off. But this just left a bad taste in my mouth. When I went to get my car, the SM said that his boss wanted to speak to me, so he took me to the back office and there was Don, the SM I have worked with the past 17 years. I thought he had left the shop; he had just moved up into management. So it was nice to see an old friend, and we talked for a while, and I told him what was going on with the car. He said that we should listen to it again revving out of gear, because he said that I know the sounds of my car better than the mechanic or the SM. So the SM brought the car into the bay, revved it up, and swore he could hear the vibration. I tried it, and I could not.
So I went for a test drive with the mechanic, pointed out the noise, and he insisted that it was a problem with the flywheel, not the axle they put in, that he had researched it, found the TSB, etc. I said that's fine, but bottom line for me, the customer, is that the car wasn't doing this when I brought it in. So we went back and I spoke some more with Don. He said that he valued our relationship over all these years, and that he really wanted to be sure that it wasn't the axle. So he said to leave the car, that he would put another axle in it, and we'll see where we are. That would be the best way to definitively rule out the axle.
I'm hoping that it's the axle, because replacing the flywheel would be a seriously expensive repair. I might decide to dump the car. But at least we'll know for sure that it is—or is not—the axle.
I can't really say enough good things about how Don handled this. It shows that there are still reputable, honest people out there in a business that has a reputation for shysters. And that forming a good relationship with a reputable repair shop can really pay dividends. I'll post another update tomorrow when I hear back from Don.