Thanks for sharing your progress. I've seen some people 'casually' recommending laser removal before getting a cover-up on the Internet. But the pictures you've shown so far definetely proof that steps like these shouldn't be taken carelessly, even when you're unhappy with your tattoo. All the best to you and I hope you will reach the desired result soon.
I think it's best to find a capable artist for a touch-up/cover-up before going too deep into specific ideas. I agree the tattoo looks better when shaved but the shape of the birds is kind of rough when compared to the fine lines of the tree underneath.