Which USB ethernet classes does iOS support

I don't think Apple has published a publicly available list. However, some manufacturers do seem to have a collaboration with Apple on USB-ethernet devices, so they probably have received documentation from Apple on what's recommended.

I'm currently working on the exact same as you, and have found that CDC ECM does not work, nor does RNDIS over ACM work. And as you describe, it seems devices using CDC NCM can be made to work. I have also tried EEM, but couldn't get it to work - that might be due to errors on my part however.

I haven't got any further information than that at the moment. If you figure out more, please update this space!