We're not sure if letting her out in the yard by herself solves the problem at all. When we refuse her, she wanders around the house looking for chew targets, as if to punish us for not playing with her. Your jrt is not looking for chew toys in order to punish you. It merely wants to do something. The dog then decides to investigate the toy.
Dogs do that by chewing it up.
It is no different than a child left alone who is bored. A jrt is no different. Frankly, the fact that your jrt wants to play with you is such a HUGE plus that you would not believe. That means it has bonded with you. You can use this need to play with you to train it and do so much.