The basic set of definitions in Nelsons (admittedly, not a specialized dictionary for Chinese medical usages) has the following:
Nelson 3799: koshi hips, loins, waist, pelvic region; small of the back; haunch; lower-panel wainscoating (lower wall only)
Afterwards come the compounds. So, a couple of questions:
First, do you have a citation in which it is quite clear that Tohei (or any other Japanese martial artist) is using koshi in a way that refers specifically to "small of the back" and not the entire region, which includes "hara?"
Second, while all these points or regions play a role in direction and alignment, how could a ground force "originate" or be "centered" someplace other than the ground? Wouldn't that make it some other kind of force if it were?
Citation? As in my response above I'll look one up for you and post it.
Secondly if you read my response earlier you will see my explanation. How can ground force be 'centred' someplace other than the ground? Well that's for you to discover. The practice and use of Koshi answers that.
Yes it is another kind of force and that's the whole point. For me put in simple terms it is the Earth energy, Ki. Ground force is not and never has been my terminology. Thus I have no use for it or need for such terminology.