I think I've solved my problem with decorating claw style hair clips! The problems I encountered were the flowers either hindering the way the clip worked, getting crushed when you try to open the clip to put it in your hair, or the open spaces in the middle of some types of claw clip providing very little space to actually attach a flower to.
The method that has worked for me so far, is to line the inside of the clip with a strip of felt so the flowers ave something to adhere to where there are open spaces, sticking to small, mostly flat and somewhat sturdy flower designs (something that you can press on a little bit without ruining), and using a flat center decoration.
I think the styles of kanzashi flowers that work well with these clips are limited, and they'll still need delicate handling.
Here's my take on it, it doesn't capture the shape perfectly, but I think it gets the idea across. Mountain laurels have a strange shape from the side that I found difficult to mimic with kanzashi techniques, maybe one day I'll figure it out! I think this one might have looked a little truer to the flower if the stamens were a bit smaller, but that size is the smallest I've got at the moment.