Go with bamboo fencing if you need a solid barrier that won't harm the earth. It shoots up fast, so you're not waiting years for it to grow like with trees. I put some in last summer, and it's already filled out nicely without much work. Just make sure to contain the roots with a barrier, or it might spread where you don't want it. Overall, it's a smart pick for anyone looking to be kind to the planet without sacrificing privacy.
My neighbor's bamboo fence has been up for two full growing seasons now. It looks solid and gives them plenty of privacy already. They went with a foot deep rhizome barrier, but I saw a few shoots escape after last spring's rains. What depth did you end up needing for your barrier to actually stop the spread for good? I've heard some types need a much deeper trench to be effective.