My take on ikkyo is that you are applying kokyo-ho through a different vector, taking control of uke's center through their elbow.
In the shomen-uchi version, I'm used to not grabbing the arm during initial contact, but extend my fingers instead, using the "te-kanana" (hand blade) which makes the bottom-edge of the hands the contact points, the same point which is critical in kokyu-ho. From there, one can begin a grip of the elbow, through which one rotates the arm and shoulder through their axis, locking up uke's body in a way that they can't rotate out of it.
From there, with uke bent over, one can go diagonally forward in either direction to complete things.
Of course, at speed this is easier said than done, as it means combining an initial large circular motion with the forward cut with a small circular rotation of the arm, all the while maintaining your own structural integrity and timing, and being very sensitive to what is going on within yourself and uke.
To escape, one has to avoid the initial internal destabilisation (kuzushi) in the first place.
Hanmi-handachi ikkyo is much harder, as the timing is completely different. In doing that, you are taking downward movement of the cut and sweeping it out sideways and forward, causing uke's own momentum to send them into the mat. The arm rotation is in there but much smaller and more focussed. That's how I see it anyway.