This is my favorite throw! At my dojo, it's called "kokyunage" like so many other different techniques. I recently learned some secrets of this technique. OTOH, I'm a beginner and maybe I'm suggesting very bad things. I submit to the collective wisdom of the forum
First, this is the AWA canon: taisabaki, taisabaki, taisabaki. It's a tenkan technique. For it to work, nage must have footwork to match the reach/velocity of uke's attack entry. Second, approach this like it was shihonage, and in fact it's great to do a few shihonage first to get things working.
Like shihonage, Uke's attacking arm will be rotated in a kotegaesh direction to reduce degrees of freedom in uke's arm. Nage has to grasp Uke crosshand, from underneath, with an upturned palm to be able to manupulate Uke's arm easily. Nage wants Uke's back to begin arching. It can help with form for Nage to get under Uke's attacking arm to apply upward pressure on Uke's attacking elbow as the tenkan brings Uke alongside. This is where Uke's balance is taken. Try this: if Nage doesn't get Uke's balance here, Uke can reverse with a sayu undo movement like sokumen iriminage.
So far, this is all like shihonage, but Nage can keep the crosshand grasp, with the kote-gaesh typerotation locking up Uke's arm to upper spine, and let go with the other hand. Nage, in this situation, has lots of options. If nage wants Uke to fall backwards, it's shihonage, but if Nage wants Uke to fall forwards, Nage uses ushirotori undo movement with a sliding step to give Uke some energy in the throw.
Shouldering into Uke's elbow will hyperextend the joint and is not cool on the mat. Uke is often a LOT taller than me, so I use more torque on the arm, and I try to bring Uke's upper arm down to my shoulder, and cut obliquely down like yokomenuchi, allowing my back foot to sweep behind me with the hip rotation. With shorter Uke, the throw can be more linear.
I'm not sure, but it seems like this could be like a kotegaesh breakfall for Uke if the throw has too much power/rotation. The forward slide into the projection seems to be an Aiki attenuation of the technique.