I tried to construct column’s proof for every nodes with the methıd Merkle Tree+Snarks. (This is the first simple method that comes to mind).

Let's say we want to prove the availability of $column_1$ for the node $n_1$. Firstly, a merkle tree is created for $column_1$ entries and $root_1$ is calculated. Then it is necessary to send $column_1$ entries to $n_1$ and the $root_1$ value. In addition, in order to prove the connection of $column_1$ with the original data, the $root_{main}$ needs to be calculated using the $root_i$ values created for all $column_i$. In this case,all $root_i$ values must be sent to $node_1$ to use it in the snark proof. The same process should be done for all nodes. In this case, if we assume that the output size of hash function is 256bit, $256bit \times \#nodes$ send to every node. Although it is slightly less than normal kzg, we will still need to send a larger amount of proof to each node.