Maybe those with a better understanding of koryu can correct me here, but wouldn't koryu be more strict in how it was taught? If Takeda wanted some free reign to "play" and keep learning, it would have been a rather weird choice for him to do so through a koryu.
So, maybe Takeda took the option that gave him the most room to do what he wanted -- create his own way using the aiki body skills. And maybe that "complex" waza was just Takeda seeing what he could do with his aiki? I'm sure even Takeda kept learning and growing in his abilities and skills.
Mark - let me answer part of your question. Depends on the koryu. For example, Kashima Shin-ryu is both strict in it's teachings, but gave someone like Kunii Zen'ya all the room he needed for free-style testing of his waza and continued research. Other koryu were really "ko" - Old - and rigidly went through the motions.
But I think Takeda was a creative, revolutionary figure - why bind oneself up in someone else's ryu when he WAS his own ryu. He had something absolutely his own. Imagine being handed a piano with only white keys and somehow you discover the black keys. Why confine yourself to the old instrument? Which leads to the speculation that many of his successors, re-confined themselves in a Japanese cultural zone - all or mostly white keys, with maybe one or two black keys thrown in. (Strained metaphor, to be sure).
BTW - I just got it on very good authority - a headmaster of one of the extant koryu that up through Taisho period - 1925 ending - a substantial number, maybe most koryu had solo breathing and other practices - but that a) a lot of these people died in WWII, and b) most ryu no longer practice c) to his frustration, even with HIM demonstrating the value of this type of tanren training, most of his students do not do it. "They don't't have time" or "I can't do that around other people. They will think I'm crazy."
As for the complex body skills, the way I've seen it - as described in HIPS - is a combination of waza giving him a means of transacting his way though society, not so simple as mere monetary gain, but the very complexity gave him the ability to teach in a sustain way for 5 - 10 days, keep everyone occupied, happy AND actually learning something - but he'd be on his way without giving away the real source of his power. AND - it think it was human origami. There must have been times that he was saying, inside, "I can do anything I want to these people. I wonder if I can stack four of them up with their feet twisted in each other's ears. Let's see!"