Your point is valid as to not being Japanese in origin, as I understand Okinawans consider themselves distinctly different, however not sure I can buy the not predating 1860. If the history of Oyata is as he says, he is a direct lineage of a family art that goes back much further than 1860. How is the antiquity of accepted "Koryu" arts any more or less proveable than that of Mr. Oyata?
The link you provided clearly states that the system was founded in the last 50 years (1969, from memory), based on what the founder was told were older systems/information. When it comes to Koryu, Japan was one of the most beaurocratic societies around, so documentation showing the lineage was fairly common, and far more demonstrable than "well, I was told it was an old family art that was only taught to one person at a time".
Anyways, my course of action is going to be to go observe a few classes and see if what I observe is a good fit for me. Seems some Oyata schools practice Bogu Kumite, which would kinda be a big selling point for me. I like the grappling and locking that I see in videos, especially the polish practicioners.
And that brings us to the question of why you've been asking if these various systems are Koryu? So far you seem to be wanting something that Koryu are not, to be honest. That's not a bad thing, Koryu really aren't for everyone. Many people would be thoroughly bored by learning a Koryu, frankly. But you seem to have an idea as to what you think Koryu are, which doesn't seem to bear much relation to what they actually are.
What are you after from your search for Koryu systems?
Alternatively there is a Birankai Aikido group not too far away. My understanding is that the founder of Birankai possessed a "harder" Aikido than others and perhaps this school may suit me. What I like about Aikido is virtually no Kata. I am 50/50 on whether Kata has anything other than a mind-body connection benefit. In my Isshinryu class sparring always turned into a mix of folly and foolishness when the instructor would prod us to "use stuff from the katas".
A harder Aikido may be as close to a Koryu as I will find, what with it's originator coming from a Daito Ryu lineage.
Okay, without getting into the quagmire of "is Daito Ryu really a Koryu?", which can be more of a headache than is required at this point, I'd say you don't really understand what kata training is, especially in a Japanese system. In terms of what the Birankai represents, yeah, it's sometimes said that Chiba Sensei has a "harder" approach than other Aikidoka, he also has a higher emphasis on weaponry, but that doesn't make it closer to Daito Ryu, honestly. For that you'd need to look for a Yoshinkan line (founded by Gozo Shioda, who left before WWII, at around the same time that Chiba Sensei was born, actually, back when Ueshiba Sensei was still teaching in a rather severe way, and his school was referred to as the "Jigoku Dojo", or "Hell School", for the amount of pain endured by the students).
In terms of your Isshin Ryu instructor's request to "use stuff from the kata", to my mind, if you're not using them, then you're not doing Isshin Ryu, you're just throwing strikes and kicks. The kata are the blueprint for the methods, tactics, strategies, movement, timing, angling, and so on. I personally don't think that many people get that, but that's me. The exact actions in a rigid form in kumite? No. But the strategies and tactics that are shown and taught through the kata should definitely come out, otherwise it's not Isshin Ryu.
Just so you know, if you really are looking for Koryu training (or the Okinawan equivalent), every Koryu's main training method IS kata. If you join a Koryu, you'll be doing allot more kata practice than in an Isshinryu class, I can tell you that much.
Some Koryu will have something like sparing in them, but they are the minority, generally speaking.
Also, I completely disagree that kata is just for 'mind-body connection', and I'm not 100% sure what you really mean by that.
The kata of a system IS the system, it's mindset, goals, methods, strategies, tactics, power generation, you name it, it's all in there. It's just a matter of being able to see that and train it with that in mind.
I tend to have a more serious attitude in my kata practice now than I did back when I was doing completions in Taekwondo.
I think he's talking about a different form of "kata", though. He trains in Isshin Ryu Karate, an Okinawan form, and, like other karate forms, takes on the Okinawan/Chinese idea for kata, or forms. That is, long solo exercises, which are not present in Aikido, and are typically not found in Koryu outside of Iai and one or two other specialist disciplines (Kyujutsu, Shurikenjutsu).
Combatisshinryu, what Sanke is getting at is the Japanese form of kata training, which is any form of pre-arranged training, typically paired combative methods with an attacking partner and a defending one. This form of training makes up the bulk of Koryu training, with sparring methods being far less common as Sanke said.