I've only been training since September. So yeah I need a lot more practice time and I'll be asking my sensei for some help with it.
Any suggestions are welcome: I'm really curious to hear what other peoples experiences have been when they encounter people with strong wrists that do not bend easily.
I have always had crazy, flexible wrists which present a similar problem, so I can testify that it isn't the wrist that you want to think about. The "pain" of kotegaeshi rarely made me take ukemi. So here are a couple of ideas from my practice.
First and foremost is to think about the uke's shoulder
not so much his wrist. If you look at the picture posted of O-Sensei, uke's shoulder is in the shikaku (death spot) where it is unsupported by uke's legs. That's important.
The second thing to think about is the spiral that the wrist makes and my guess is your spiral was too small. Once you have a connection to uke's shoulder through his hand, your spiral will move his shoulder off of his hip, taking his balance and starting his fall. The spiral can be vertical or horizontal, (Probably other things, too,) In other words, the connection can either dislodge uke's shoulder toward his back or draw it out in front. Your movement can help determine this. (Look where O-Sensei is in that photograph.)
Lots of good advice out there. Try it all. Wear what fits for the time being and store the rest.