I'm personally not too worried about the Moon Druid damage, because you are forgetting that they get +2d8 damage from the base class. So that mammoth is hitting for 6d8+7 which... yeah, even at level 18 that would make someone sit up and take notice. That's 34 damage on average. And even weaker beasts are going to be doing decent damage with that.
The bigger problem is accuracy. And I think calculating the Wildshape forms attacks and damage using Wisdom makes sense. You get your proficiency too, so the mammoth is rolling at a +12, which is real good. But when you look to the wolf, they would be a +7 using the proficiency, and I'd rather see that as a +9 or 10 by those levels.
hmmm.... 2d4+2d8+2 = 16 damage... that's a bit wimpy. But you'd be a dire wolf and 2d6+2d8+3 = 19 isn't bad. Firebolt is likely doing 3d10 = 16.5, maybe adding the int bonus. The damage might be a little lower than we'd like, but it isn't terrible for a full-caster.
That and the wild shape temp hp... Yeah, I think if we really wanted to make the damage great, all we'd need to do is make the druid add their wis mod to damage, and be able to use their wis spell attack to hit, but the proficiency swap and the extra damage dice are doing a good bit of work.