Hello Eilidh and welcome to our family and congrats on giving Chippy a new forever home.
I hope you are going to make avian your speciality as we can always use more qualified avian vets, many members here have difficulty finding ones that specialize in birds and they need people who know more about them than just an animal vet. There is only one in my area or I would have to drive for several hours to reach the next closest qualified avian vet.
You already know what you should be doing so keep up the good work and in time Chippy will come to trust you, patience is key.
He can have lots more vegetables than just some greens and parsnips, there is a thread in the bird food room that list many of the ones he can have and I would go lightly on the fruits as they contain more sugar, don't feed fruit every day but its good he is eating a good pellet. He can also have some grains, legumes, rice, pasta, a little chicken now and then and some egg.
I look forward to seeing some pics of him and that video you spoke about.