Unfortunately I think that the only way the DAS scheme can work is if the light node actually downloads the samples directly. I don’t think you can get around this requirement by using a zk scheme.
However, there are ways in which we can use zk to improve the DAS scheme. A big one is what you mention above:
generating zk-proofs of correctness of erasure coding itself
If you created a way to generate a zk proof of correct erasure coding, then light nodes would not have to wait for a fraud proof window after sampling each block to consider it final. Second, we wouldn’t need bad encoding fraud proofs (BEFPs) which require the light node to download an entire row or column of the block data. Third, this unlocks the possibility of having consensus nodes vote on blocks without downloading all the data.
I think this would be a valuable thing to try and build. I talked about this and other zk based improvements to Celestia in my talk at research day: https://www.youtube.com/watch?v=NCLuU-NS3IU