I haven’t dealt with a rink without a liner but here are my thoughts.
I’d try and get a couple thin layers down while it’s cold to seal up the holes you have. Then after they’ve frozen solid put some heavier layers down to build it up. Use hot water if you can. That’ll help to knock down some of the bumps.
I just think you need to keep adding layers. Even those holes where the water is running through need to seal up eventually. I think it’ll start to even out too.