I do feel for you over this one, I just wanted to say that by law you are allowed a 7' fence without planning permission but do consider any neighbours and the cheapest way i have found of adding extra height is by using a trellis which can be added with batten to the supports of the lower fencing
The other thing is a tether in the garden is fantastic if the dog is being watched, if they are unattended please don't do it in case it gets wrapped around his neck

.
It sounds like you are making real progress on the stop whistle which is a huge achievement, keep focusing on that and don't let him in the garden until the fencing has been heightened

.
Can the rescue give you any help/advice with his training, it's always worth asking?