I live on a corner so one side of my backyard is exposed to the road. Pic related. This is actually an old picture of my fence. Before I bought it someone stapled on chicken wire presumably so it could be marketed as a backyard one could have a dog in.

I'm wanting to remove the chicken wire because it looks like shit and makes mowing difficult. The problem is that one of the cross sections on my fence has shrunk and is only held up by the staples in the chicken wire. It's floating for lack of a better term. Held on only by the chicken wire.

This fence has been falling apart for a while. There used to be a gate. It latched on a standalone post butted up against the house. That post rotted out. One day the gate got pushed shut and the post snapped off at the base. I tried to replace it but the concrete footing was pretty far in the ground. I dug around it with hand tools but there was no way I was going to be able to get a chain around it because of how close it was to the foundation of the house. The earth around that area was clay down towards the footing too. I said fuck it took off the door altogether. From my experience with the one gate post, the footings are not cylindrical. Just blobs of cement in the earth.

I want to remove the chicken wire. If I do this I need to replace one of the cross beams because it won't have anything to "float" on anymore. The new cross beam will be a wildly different color as it will not have experienced the same weathering. I don't want that. I could replace the whole fence but trying to lift the post butted up against the house was enough to deter me. What do?

One thought I had was to "extend" the shrunken beam. I could wood glue / drill some kind of cap on it to make it fit. It still wouldn't match the color / aesthetic but it would be much less noticeable than replacing the whole beam and would probably only take an afternoon.