Hi,
While there's a lot of info out there about the Hon'ami and Fujishiro families (probably because they're still active) - I can find very little about the Takeya and Kiya families, although the NBTHK named their top polishing prizes after them. Does anyone out there have more info on these two families? As far as I know, they both stopped working in 1876 - due to Haitōrei. Fujishiro is a relatively new school so from Muromachi untill Haitōrei you had 3 main families, Hon'ami, Takeya and Kiya.
Kiya was the polishing family that worked closely with the Tokugawa shogunate, so I expect that there would be some info out there, but I'm unable to find it. Their lineage before the 16th century is doubted, but from Tsunenaga on, it seems to be documented.
I've found this small essay, which seems to hold some basic information, but I'm unable to translate it coherently - maybe some of our more fluent Japanese speaking members might be able to help out? http://www.mokuzai-tonya.jp/05bunen/zuisou/2006/02nihontou26.html