I would ditch stewardship, or, rather, I would make stewardship a function of defining boundaries.
Lunars are the Mirror, the Other. They are what you are not. No matter what you are, they can become something you are not, what you wish or what you fear, always more to their advantage than yours. They are the Exalted of the Wyld, the Chosen of Dreams, the god-monsters of the world's hidden places.
(Did you know that "shinma" is a word originally created for a manga called Vampire Princess Miyu, and is the pronunciation of the kanji character for "god" together with the kanji character for "demon"?)
They are bound to Creation because the reflection cannot exist without what it reflects. Inasmuch as they must protect Creation, it is only because of this.
Their shapeshifting would become ephemeral rather than fleshy. Chimerae would change greatly — less mad amalgamations of multiple forms and more reflections distorted by a storm-rippled surface.
In other words, I'd move them back towards the only niche that's actually open to them in the setting — potential lords of the Wyld infatuated with the Solars, with every Lunar Exaltation forged from the reflection of a Solar Exaltation's brilliance, just as Luna herself was created to reflect the Unconquered Sun. Their transhuman endpoint would be a lot more gazellecarp or Air Body Style and a lot less kaiju.
The Lunars were originally conceived of as the Fair Folk. Then they were conceived of as one-and-all the crazed allies of the Fair Folk. Then Geoff decided to make them playable and they ended up the 1e Lunars.
Then they became the 2e Lunars.
Both the 1e Lunars and the 2e Lunars suffer from not really having a place in the setting, because the rest of the setting was designed around them being either the Fair Folk or the allies of the Fair Folk, and then they were made into a playable group when the setting had solidified.
So I'd just revert them to something approximating what they were back when the setting was created, and fit them back into the hole they left. They'd have a place! Plus, with Jenna's work, it's a lot easier to take something in that place and make it a playable and mixed-group-friendly nowadays than it was back when Geoff decided he needed to completely remove them from that millieu if he wanted to make them playable.
It does kinda stomp all over the Fair Folk, but I've been of the opinion that the Fair Folk need a reconceptualizing since Fair Folk 2e hit. Jenna's work on Fair Folk 1e was brilliant, but too niche, and it's almost impossible to stay true to it and create a solid product.
It's not as simple as making them Fae Exalted, though. I'm convinced you can actually do all this while leaving a place for the Fair Folk and keeping a place to play Lunars the way they tend to be played now.