Something like Sweet Autumn clematis might be good. You have to cut it back each
spring anyway, and if you decide you need to move it, that would be a good time to do it. It's vigorous and could cover your
tree in one season.
I picked up something new this year, it's a black-eyed susan vine. I'd never seen it before, and it's an annual vine here in
zone 4b. Morning glory vines are also annual for me. Of course, both the above mentioned vines
flower.
You could try something like hyacinth bean or climbing spinach. That would be different.