For example, Waadi is down 3 points each of Body, Mind and Soul. They also have stat damage to Spirit. They would roll Body and Mind normally to regain those points, but instead of gaining points of Soul, They make the check for Soul to heal the point of Spirit damage. They only regains the point of spirit with a critical success, Correct?
This makes damage to Endurance, wisdom and Will extra perilous and the need for Medical attention very important.
If you restored 1 point of Stat damage for SPI, you'd still get the "auto" heal for a long rest. So, for Soul healing, you'd still recover points equal to your WILL. You just wouldn't get the additional point from rolling the WILL healing check.
What's ambiguous is how many attempts can you make per short rest to recover Stat damage. The rules say that you can only restore 1 point of Stat damage across all Stats per long rest. You could read that as you can make 1 attempt to restore Stat points per long rest. Or that you can have only 1 successful Stat heal per long rest so that if you failed to heal SPI, you could then attempt to heal AGI. I can see the intention as 1 attempted Stat heal per long rest. But as written, the second interpretation seems valid.