Natural lining in a clay pond

Hi there! I hope you guys can help me, this ia my situation:
I have a pond digged in a very clayish soil. It's basically only clay, very greasy one. There is a little spring upwards, so it seems into the pond and there is a pipe for the overflow, the idea is that the water goes in and out. The main issue now is the lining of the pond. I thought that with so much clay it will not be needed, but when it's wet, it turns into sliding mud. So we have a lot of loss of water, so much so that it doesn't even reach the pipe for overflow. And the pond is very muddy. On top of that, the walls of the pond are definitely too steep, however there is no way to fix that now with a digger and hand digging in this clay is way too heavy.
My last hope is to plant some water plants, perhaps they will help with the muddening and water loss? I don't want to use any plastic, concrete would be one of the last things I want to use, bentonite is too expensive and I don't think it would work on this ground anyway. I don't know, do you have any ideas?

Thanks!

Maja said, "I thought that with so much clay it will not be needed, but when it's wet, it turns into sliding mud. So we have a lot of loss of water, so much so that it doesn't even reach the pipe for overflow.

You might need to borrow a pig or some ducks to "glee or gley" the pond.

https://permies.com/t/38201/Progress-Gleying-Pond-Pigs