Keep trying with the fruits and veggies.
My own Sammy was super stubborn at first, too. I found out that he liked the veggies whole instead of chopped up or messed with. So I put whole cilantro and parsley stalks, lettuce leaves, a bit slice of carrot, a slice of mandarin, etc. I've also taught him that me saying "yummy yummy" means that it's delicious by eating whatever I offered him while standing next to his cage.
It's normal for even a hand-trained budgie to fly away if he senses that you are going to touch or grab his sensitive spots - head, back, belly, etc. You can just rub your finger lightly along her belly to see about the fat deposits.
Try weighing her next to her cage where she's more comfortable. Or put it at the bottom of the cage with some millet on it if you want to get really crafty.
Good luck finding an avian vet! I'm so happy with mine (in Madrid) and am glad that I've got a good relationship with the clinic in case of emergencies!