I think I may have found it: TeX Gyre Schola, a free Century Schoolbook clone. It’s been around for years, which hopefully has given people plenty of time to work the glitches out of the thing. (Glitches being the bane of open source fonts, and one of the reasons people still pay for commercial fonts.)
Century Schoolbook, like most of the serif fonts in the Century family, is a modern serif font. It’s not exactly the sort of modern serif font I typically really like; glyph sizes tend to be wider and the variation in the font weight less than in typical 19th century typography. Both were of course deliberate design decisions made in the name of creating a font easy for children to read (it’s not called Century Schoolbook for nothing).
However, those minuses tend to become plusses on the Web. Even the best screens pale in comparison to the resolution a low-end laser printer (much less a printing press) can deliver. That makes reproducing the fine details in most modern serif fonts tricky. So the very same features that make larger sizes of this font easy for beginning readers tend to improve on-screen legibility for smaller sizes of it.
Being a TeX font, it has a lot of glyphs, which makes for larger font files and slower web download times. If anything makes me dump the new design, that will probably be it.