But Tohei Sensei was a very clear, plain-speaking teacher. If he meant "koshi" he would have said "koshi."
I will grant you that by "centre" (as in "drop one's center") he probably did not mean the same thing as "one point" (as in "keep mind at one point") or he wouldn't have used a different word.
I can't think of anything in Tohei's teaching to suggest it is the sacrum/sacroliliac area.
In my own practice, I experience the "centre" as being that entire area between the diaphragm and pubis, encompassing front and back, a large globe if you will, resting on the hips, with the one point within it.
I still don't get the "koshi" thing outside of your system but that's ok - I think we have each clarified our language and usage and may have to agree to respectfully disagree.
I agree with what you say.
I can only point out not only what I learned but how I learned it and the explanations given.
As you are probably aware I was taught with emphasis on the Tohei principles and my teacher was English. However he taught us within that framework Koshi.
Now on researching it I find it is not only well known in Japan but traces back to the origins of all Japanese martial arts.
I find this quite amusing as I have often pointed out to people how it makes early Judo and Sumo make sense.
I do remember early on my own teacher wondering why we wern't duplicating what he wanted us to do and then him realizing we had a different view on what using the hips meant. Thus our introduction to Koshi.
Anyway. Hopefully it's interesting at least and for some it may explain a few anomalies they have come across.
To clarify what I teach for others I would say that koshi is the centre of relaxing energy and hara is the centre of vibrant energy.
It would be interesting to know if or how often Tohei mentioned hips.