The latter is I think aiming for Linux ABI compatibility.

I had never hard of Asterinas, but this sounds like a the best approach to me. I believe alternative OS’s need to act as (near) drop-in replacements if they want to be used as daily drivers. ABI-incompatible alternatives might be fine for narrower use cases, but most people wouldn’t even try out a desktop OS that doesn’t support most of the hardware and software they already use.