I'm having similar problems. I added water lilies and some other plants. I don't know what size your koi are, but mine were small when I added the plants. Thankfully to date they don't bother them. You have the problem of depth. How about some floating baskets? You'd need a lot but worth a try. Or you could try the dreaded 'weed' - water hyacinth - which no one seems to be able to successfully grow, even though its a weed (can you tell it frustrates me?!?!?!). My koi do eat that. But they leave my potted plants alone.
Do you have any kind of water catchment area before the water goes back into the pond? Waterfall bucket, small pond - something like that? You could plant that if you have it.