So I looked at a few videos on doing this and it looks like a real PITA. Pulling the ends out looks like the hard part, and I'm not sure I want to risk breaking them or marring them trying to get them out.
I called Starrett (nice people, by the way!) and they quoted me an estimate of $87 plus shipping to overhaul it. This includes "changing out the vials, scraping the base and putting it into tolerance", according to the email they sent me. It has two other bubble levels on it and one (the one below the main vial) looks like there's no bubble so it might be worth it. The bubble level assembly is $117 plus shipping so I'm not sure how they can quote $87, but I guess I'll find out.
This was my grandfather's so it has a little sentimental value, so I think it's worth it to fix it, especially now that I need to use it. It's been sitting for about 20 years and I'm not sure how much he used it.