Since the tree obscures the view, why not leave it as is? Let the wood weather like the rest of the fence.

I cannot tell exactly how that one trunk leans over the fence, but do you think the neighbors might let you mount the remaining panels on their side of the fence, if that would help? or:

these wouldn't match the rest of the fence, but would give you privacy. Wattle around the trunks:

flexible fence woven in amongst the trunks. This might disappear in the shadows

Love your input. Thank you! Here’s my thought, I don’t want to leave it as is because the tree branches will take a long time to fill in since they were chopped down last month. As far as providing a wrap around, I think it’s a viable solution, although I question how it may look, especially in the winter when the leaves are gone. I appreciate your input. Keep them coming!

It would be best to talk to your neighbors about the many-trunked tree. It looks like there are already stumps nearest the patio. Trunks growing toward the fence or already hitting the fence are going to get bigger. An arborist can identify which trunks can be retained and which should be removed. Maybe some of the skinniest, newest trunks could be trained to lean away from the fence.

In the meantime, a flexible canvas could be made and installed by an awning company behind the trees, like a cloth version of the wood privacy panels. It might be good for a few seasons, depending on climate and wind.