Would be really thematic if Udyr's Phoenix Stance active healed up Grey Health.
Plus, would create a bigger divide between Tiger and Phoenix stances.
A higher percentage of damage taken could be translated into Grey Health while in Turtle Stance. The heal on Turtle Stance could also heal a small portion of Grey Health instead of increasing with missing Health so it isn't just visual clutter to Tiger Udyr pre-level 16.
The amount of Grey Health healed up could scale with Phoenix rank and/or Ability Power so Tiger Udyr can put one point into it for the heal, but it isn't always a good choice.
If the heal on cast is too non-interactive or powerful, it could be a heal on hit and every third hit instead. If Udyr has too much access to regen overall with these changes, his W hit and every third hit could grant a shield instead of healing, the heal could be reverted back to Life Steal or it could scale with Attack Damage or Armor so it's better on Tiger Udyr.