So I thought I would write an update as to where things are now. I took it to a local machine shop. The guy there was really friendly. He doesn't have a tool that could pull out the bearing, as he said there isn't enough there to grab onto. His idea was to heat the whole housing to 400 degrees, drop it on a piece of wood, and hope that the shell falls out. This is probably based on the fact that the aluminum housing will expand more than whatever hard metal the shell is made out of. However, he didn't want to do it with the pinion in place. I looked into removing it, and it sounds like a can of worms that I'd prefer not to open. As it is, it turns smoothly, and I can't feel any play. Over the years, I've learned when to leave well enough alone.
Back to square one. I was considering modifying the HF tool, but I'm worried that the 3 claws won't provide enough surface area, and if I grind them down, they won't be strong enough and will snap off. Now that I found the real tool that you're supposed to use (more on that later), I see that the HF tool is not just like the official tool.
So I followed the links provided here (thanks guys) and was able to find more info about the official tool. There are two pieces--an "internal extractor", which is kind of like a pipe with a lengthwise cut that flares at the end and spreads when you tighten it, and a "counterstay". A scoured the internet trying to find these tools at a reasonable price, and the best I could find was about $65 for each at a VW tools site. After tax and shipping, $152. Ouch. Still much better than $300+ at other sites, though. Check out the internal extractor here:
https://vw.snapon.com/SpecialToolsDetail.aspx?itemId=51330007I ordered it. Normally, I wouldn't fork out that much money for a specialty tool that I'll probably only use once. I just don't think I have much of a choice otherwise. It's the only sure-fire way to get that thing out. For that price, I could get another used final drive, but with no guarantee that its race is in any better condition. Oh well.