If a dog is happy and doesnt have any issues then it makes no difference if the fence is two foot or six foot, IMHO. My dogs are very happy but a two foot fence would not even register to them that it was a barrier :-) Both my dogs are rescues and both have unsupervised access to the garden which is enclosed by a six foot fence. In dry weather the back door is never shut and the dogs have unlimited access to the garden and they choose to spend a lot of time out in the garden. It would be impossible to always supervise them out there
and let them enjoy the benefits of choosing to be outside if they so wish - I do have other commitments in my life as well as the dogs :-) They are never left out in the garden if nobody is home though - then they are shut indoors.
The rescue from which my dogs came from insisted on high fencing as they had no idea if the dogs were well practised in the art of escaping. Our larger rescue was just a pup when we got him so he was physically unable to scale the fence and has never tried to even though he can easily scale the groynes at the beach which are far higher. Our smaller dog was not a small pup when we got him and had never been out in a garden so everything out in the big wide world was new and exciting and his for the taking so a high fence was a necessity for him.
Taking on a rescue dog is far different to having a puppy from it's breeder and training it your way - one often doesn't know what one is taking on, as indeed the rescue does not always know for certain the full characteristics of the dogs they rehome, because these characteristics often change as a rescue settles in to it's new home and gains confidence.
Could you not fence off a smaller area for the dogs that has a higher fence and thus prohibit access to the rest of the garden?