Thanks for the offer, but we've been down that road before. I'm frankly still wondering why lunges and turning the body suddenly becomes axis training and 'internal' strength and when it is Japanese or Chinese natural suddenly people don't know about it except for a select few.
That is exactly what I could help show you
The lunges/turning the body in shintaijuku isn't just lunging/turning the body, that is simply copying the shape without the intent. If you do that exercise correctly, you will find that the body starts to push/pull itself as you "open" and "close". That is to say you aren't mentally telling the legs to push, they just start to move as though it was of their own accord.
for example in shiko (the sumo stomp exercise), when closing the right arm, you start to find the left side of the body turning. If you don't have the right alignment/structure etc, you don't feel any of these sensations and as a result each part of the body starts to move independently of the other instead of as one unit.
When each part moves independently instead of as a whole, the resultant strike/throw etc isn't quite as powerful.
If you want to check out the swordfest 2007 demos in Alexandria this weeked (http://capitalareabudokai.org/swordfest.html
demos of eastern and western sword styles, chinese, german, italian, japanese etc), I will be there and if you have 10 minutes to spare I can hopefully answer the above question for you.