I'd suggest less hip turning and more turning from the waist with the feet remaining stable. Power will then transfer in a different path. Rotating on the heels is not something I would ever be doing in any type of training- for any reason.
Since long weapons were brought up, it might be worth mentioning that turning from the waist and drawing "through" the hips (with hips more or less remaining with a forward orientation and mobility is a necessity in Japanese long weapons.
The large hip turning you are doing in your Shintai jiku is also seen in various Iai, Aikido and other modern derivations of body arts. Hip turning and locking the knees to the movement of the hips (and for many the shoulders with the hips as well) has become part and parcel of many arts as they get more and more Kendo-ized, judo- ized and Iai influenced over the years. It just won't cut it with long weapons.
The hand positioning becomes indicative of certain body attributes and "palms up" as a constant-I would offer is an invention of Nishioka and is not something I would recognize as being needed for sword or any other weapon. In fact hand positioning and where it occurs in relation to the body change is key there. So I would say just the opposite is true from the "palms up" example. Overall, modern weapons traditions and their re-creation of certain body mechanics are in many ways antithetical to the older Koryu-more particularly the Sogo bujutsu. FWIW, this is not my opinion. There are specific discussions to be had regarding body skills and power generation and the use of long weapons with people experienced with Japanese weapons. Large hip turning is simply not a part of that discussion for several reasons.
It’s tough not to get into a right and wrong discussion, when some things are so blatanlty obvious. When swinging a naginata; if you power it from, and turn from, the hips - you then need to re-adjust for your next forward move. That means you're open to a counter strike. Without getting into details, using the waist is both practical and teaches a way to develop a duality of power generation-out and negating power coming-in that leaves you neutral in the process. All while offering both the ability to make change in all directions and to keep moving in all directions present at all times. Something which-I think for those who train heavy weapons at full speed- will appreciate right well!
How does all of this morph into body skills for modern methods; everywhere.
Interesting Points Dan Thanks
...FYI Nishio did not "invent" "palm up" and it's not so much palm up as "holding sword in hand" Tai Jitsu...I should have clarified this better but I was referring to Chris's Specific Movements in the You Tube and our training paradigm...The Arm is an extension of the Sword/Jo and not the other way around from the point of view of "structure"
Hopefully that helps clarify things a bit.
Happy Holidays and Hopefully I'll get a chance one of these days to put flesh and bones towards understanding your excellent expression of Aiki.