I was looking around at photos of a different kit (the OLED watch one, completely separate from the ones in this project) trying to figure out what MCU they're using, and came across the website of what I assume is the original maker of these kits. It probably doesn't offer much more than what's already known here, but it might be an interesting resource.

http://www.diyleyuan.com/JC/
STC15F204EA (non-voice): http://www.diyleyuan.com/JC/01.html
STC15W408AS (with voice): http://www.diyleyuan.com/JC/HJ1.html