The author tried essentially the same thing as what you suggest. He booted into recoveryOS (a separate partition) then from there tried to delete files from the main system partition. But rm failed with the same error "No space left on device". So as others have suggested, truncating a file might have worked "echo -n >file"
The next step I have used and seen recommended after recoveryOS is single user mode, which is what I think I used to solve the same issue on an old mac. I vaguely remember another reason I used single user mode where recovery mode failed but I do not remember any details.
My bet is that you can get nearly the same functionality with single user mode vs booting from external media, but I only have a vague understanding of the limitations of all three modes from 3-5 uses via tutorials.
