A junkpole fence might work as long as you don't have an HOA to whine that it isn't manufactured. Since you are only needing to add height, I think it would be possible to build the junkpole fence around the exterior of the existing fence to prevent the dog from trying to chew at the poles and add height
enough to ensure there is no way for the animal to jump over.
As to the price, I have no idea what someone would charge to do a junkpole fence, but there are people here seeking badges in the
PEP who could possibly help themselves and you at the same time. If a
permie lives near you who is needing to meet the junkpole requirements, they might even do it for little to nothing as a way to get their badge requirement taken care of while also helping a fellow site member. Just a thought.