With all usual disclaimers in effect (..These are only my thoughts. No guarantee.)
I think what you are talking about is the feeling of a traveling blood/pressure/flexing wave modulated by your body. The same pressure/tension wave mentioned, with respect to ki, in Fune Kogi Undo. The feelings of "pseudo-mystical stuff", as you said it, are what I take to be your awareness of the blood flow, the compression due to the external load, and the ground paths (jin paths?) thru the loaded body, all combined, effectively, into one focused point, and the interplay between these factors.
The physical load is transferred (in/)to the Effort System, as mediated by your intent (/spirit), structure(/dantien) and effort(/ki).
Then it becomes the effective virtual load, as borne and experienced by your body (and mind).
What do you think?
There are associated feelings of "pressure", "tension", blood flow, etc., but not in the ways you're talking about. For the time being I am quite happy with my original statement---but maybe with a bit more emphasis on the "might" part, since feelings change over time:
If you're focusing on the connection between the legs ... then it might feel as if "something" is being "passed" from the leading leg to the trailing leg through the lower abdomen.