Jim, I think your biggest challenge here is to play with the exposure a bit. I'd darken the front of the tree and lighten the BG a bit to separate the two from looking so much alike. The bottom left corner of the frame seems to be a bit overexposed and the upper right of the BG seems to be a bit under exposed. I'd play around with those two areas a bit and see if you can find a better balance.
It is ashame about the bill being over the bark - I tried to dodge it but it's so close to the same colors it just won't really come out any better. Such a lovely bird! I wish I had some in my yard.