The shihonage that I worked myself into has me drop center as I enter under the use's arm, as I turn to the outside I stay down, keeping the held wrist/hand circling out and around, with the arm brushing the top of my head as I pivot through. I keep the arm out and extended to keep uke on the edges of their feet and destabilized.... If I dropped further anytime during this motion or just pulled down it would likely result in damage. I take use's wrist/hand right back into their shoulder.....once that is reached I do what some might call a scissors cut.....stand up and bring my hands to my waist as if cutting with a boken. My center rises up as my hands/arms come down to meet. If uke has been destabilized this motion drops them right at my feet with no injuries and without giving them back their center.
from nage's side, I recognise your description as very similar to the way I approach things.
Where things may differ is in uke's part. As I described in the 'following' thread, as uke, I would follow all of nage's movement and their attempt to stretch and turn me. I do see, via video, that many uke's stand pretty stationary and 'let' the technique be applied to them. Either way, shihonage is a technique that is effective if applied correctly, as well as easy to get quite spactacularly wrong.