Good news about the vet. Like you, the closest avian vet for us is over 2 hours away. There is a closer vet who will "treat" birds and I use her for nail trimmings etc. When Timber needs a real check-up or were to seem ill in anyway, to the avian vet we go.
I have a picky eater too. You just have to keep trying and you will find things Joey likes. Also, it is very early days in your relationship. He will probably be more receptive to new foods when he is comfortable and relaxed in his new environment. This can take awhile for a grey. Timber will eat cooked sweet potato, a bit of raw carrot and broccoli, fresh peas in the pod, and a bit of raw cauliflower. Those are his standard "will almost always pick a bit" veggies. He also, strangely enough, likes artichokes. I buy a whole artichoke in the produce department, cut off about an inch at the top and about 1/2 inch at the bottom, strip the outer leaves (to aid cleaning), wash it well and hang it on a skewer in his cage. You really have to experiment to find things they will eat, and often they will eat something one day and not the next. Just keep putting it out there. Timber also wants whatever I'm eating, so if it is safe for him I give him a bit.
You can also try a boiled or baked chicken wing with most of the meat stripped off, egg white, etc. Timber is partial to meat, and it is good for him in small quantities at least. When we eat out, I always bring him home a little piece of steak, he is really partial to that.
You might also try feeding Joey off of a spoon. I don't know if it is because most of them are hand-fed by breeders and retain memories or what, but Timber will at least stick his beak in anything I give him on a spoon. He may fling it (like he does yogurt) but he at least tastes it. Sometimes he will lick the spoon clean!
It is trial, error and persistence that wins the day with diet.