The funny thing here is that I find Takeda sensei's and Dan's training approaches very compatible.
Takeda sensei's physical ikkyo and iriminage are awesome. What do you do when the hardest techniques are mastered? Take them to MMA - okay if you like that. If you are a teacher and don't know how to best teach that kind of physical structure/mental intentions directly then maybe you work on extending the connection to the point that your students start practicing some of their lines of intention.
With Takeda sensei, I've seen personally withnessed his approach to teaching to take things to an exteme (Dan does too by the way). I will say training like that - okay not so far he wasn't touching me at all - but continuing to stretch out toward him as I fell away actaully helped me quite a bit with getting my mental intentions "strengthened" (not sure if that is the correct word!) when working with Dan.
As a side note - that actaully seems tangenially related - I would like to address this:
So Dan chooses to let no one see what he is doing unless they are working with him one-on-one in circumstances over which he has complete control, and that's quite understandable.
I just want to talk about this part: "he has complete control". I want to disagree with this because I believe that Dan goes to BJJ and other MMA places and works out with them playing by their rules - whatever they may be.
On the other hand, I also agree with the phrase "he has complete control". It reminds me of a story when some HVAC guy walked into the dojo (I rent space) and demanded my attention while I was teaching yelling to me. The conversation went like this:
HVAC guy: "ARE YOU IN CHARGE HERE?!" - (I stopped teaching)
Me: "Yes." (I started approaching him to help if I could).
HVAC guy: "DO YOU OWN THE BUILDING?!"
HVAC guy: "THEN YOU ARE NOT IN CHARGE HERE!!!"
Me: "I'm in charge everywhere I go." I said it very softly. At this point I was standing in front of him. And he chose to calm down.
I used the things that I value from training with Dan AS WELL AS the things I value from training with Takeda sensei.
YMMV - Rob