I don't know about he use of koryu"ancient style" , but the Seibukan, if it is Okinawan would refer to Seibukan Shorin ryu which was founded by Shimabukuro Zenryo,(or Zenpo), one is the son, was a student of Kyan Chotoku. He founded his branch around the 1950's if I remember correctly.
I am not sure why they would use "toude, and karate do " together. toude is an old word for the Okinawan art, and karate do is the newer( as of 1936). Perhap they are trying to make is sound more authentic or older. I would check their credentials.
The only other Seibukan I know of is the Seibukan international in Japan, which is a Goju ryu school founded by Suzuki Hanshi,(now deceased).
Some of Fuse Kise's students that branched off still call what they teach Shorinji ryu, because Kise Hanshi used was a student of Nakazato's for a while and went back and forth. He has master rank in both Matsumora seito Shorin ryu(from Hohan Soken) and Shorinji ryu.
He now calls what he teaches Kenshinkan Shorin ryu, and or, Matsumora seito Shorin ryu.
I realize this is a quite lengthy response, but I tried to give you in depth information.
Shorinji ryu, does use some deeper stances than, shorin ryu. Now, Japanese Shorinji ryu is a whole other animal in itself. Its more of a full contact, sport style karate with a traditional base. Depending on which version/school of thought you run into.