Re: Soft vs hard (correct?) kote gaeshi?
The "soft" version of kotegaeshi described in the original post is the method we use (Hakko-Ryu Jujutsu). Both of our thumbs are on top uke's hand and we press it straight back and down to a point directly next to their foot. We turn uke's wrist out slightly and never bring it above our waist.
This method avoids any permanent injury and you can apply it at full speed and with a good deal of force. It occurs pretty quickly as well so uke never has the opportunity to do a big breakfall out of it.
Our method is similar to a method of kotegaeshi I've seen performed at an Aikikai dojo, but they used the palm of one of their hands pressed on top of uke's hand with the other controlling their wrist.