I *just* figured this out, so bear with me. It's newly stolen from one of the senior dan ranked students at my dojo...
Approach the shihonage like you were going to do this kokyunage:
As I have learned, the secret to this throw is rotation of uke's arm to reverse the elbow joint, stiffening uke's arm, making it a cantilever against nage's throwing shoulder/upper arm. Once you get it, options begin to dawn.
In this kokunage throw, if nage's grasp rotates uke's palm forward and up, it takes up all of the slack in uke's arm. At the point when nage has loaded uke's shoulder as a fulcrum atop nage's upper arm, instead of projecting uke in the kokyunage throw, maintain uke's arm rotation and nage can reach around to grasp uke's hand with both hands while stepping the leading foot into position to execute the shihonage throw. With the two handed grasp, nage can just opt for shihonage instead.
At this point uke has very little flexibility in his arm, and if that stiffness (connection to center) is maintained, less than halfway through nage's pivot through shiho, uke's balance will be broken irresistably and effortlessly. When nage has completed the pivot... let's just say that's the magical feeling... uke suspended.
You can tell that Tamura sensei is doing it in this video.
Also it seems to be the extra secret sauce in this Chiba sensei demonstration.