I finally took a few hours and put together my JYE Tech Capacitance Meter Kit. It was a pretty simple build. Some folks on Amazon complained about the instructions but things seemed to go pretty straightforward for me.
It basically seems to be a version of this ELM-ChaN circuit. I tested it out on a few old capacitors I can still read the markings on and it seems to work just fine. Now I can check out some of those that I can't read :)
Next step: Mount it in a mint tin or some other small metal enclosure.