Sorry if this is late, been busy at work. Also sorry for any confusion.
I train with Mr Lindsey. I hold rank in both Matsumura Seito, and Hakutsuru White Crane. Those aren't the full Okinawan names, if you really want them I can try to dig them up. I was never good at remembering terms. But the point is, those are 2 separate styles Mr Lindsey teaches. While studying Shorin Ryu, he also studied and researched Okinawan White Crane. He has (along with others, some of which were already mentioned) collected a lot of crane kata from different sources. We have 2 kata called Matsumura Hakutsuru (Sho and Dai) and I think those are the 2 which came from soken through nabe. As for a secret family kata, I know what you're talking about, but the only part of the name I can remember is machimura. That kata is considered Matsumura Seito, not White crane. There are a lot of crane elements in it, but then again, there are a lot of crane elements on most of our kata the way we do them. Mr Lindsey has done videos of some kata with explanations, but I don't know where they are and if they are currently for sale, I would be surprised.
I'm going to stop typing now because I just remembered there is a bio on Mr Lindsey at : http://www.oldfightingarts.com/AboutSensei.html
This website is maintained by one of his students. I don't remember who wrote this bio, but I know Mr Lindsey has seen it and if there were any glaring inaccuracies he would have had them corrected.
Here's an excerpt that's relevant to the question that was asked about where Okinawan White Crane came from:
In the 1980ís, Sensei Lindsey began extensive research on Fukein Chinese and Okinawan White Crane Karate styles and systems. Eventually this research led Sensei Lindsey to Grandmaster Takaya Yabiku. Sensei Yabiku had been a student of Hohan Soken for about 20 years and had researched the White Crane Styles of Okinawa in great depth.