Do want. This is a good idea.
I assume these Tattoos function like Lunar Tattoo Artifacts that are already canonical - they have to cover the area they effect with appropriate imagery?
Does the Lashing Vine Tattoo actually give +2 Dexterity? If not, then it's fine (perhaps a little high on commitment cost?) If so, it's harder to say. Tattoo artifacts are allowed to be a little stronger than normal, given that they can't be removed or easily hidden.
Fire Body Tattoo: Stop it with the new rules! We have terrestrials charms for this!
Good idea, though. How is this particularly Lunar-themed, however? If it's not, perhaps it is in need of a flavor upgrade to make it so.
I would recommend some smaller tattoos - these seem to both be full body, and that's much more annoying. Perhaps a lesser Flaming Hand Tattoo, for the damage bonus to unarmed attacks but no more.