hi, the problem with the birds beak overgrowing may be because he is ageing and while he may still have many years of life left when they get older they tend to use up more minerals and vitimins in their body , it usually suggests fatty liver disease which the main cause of is by eating to many sunflower seeds which are very high in fat, my birds have basic diets with a limited amount of sunflower seeds carefully weighed up and added to a different pot , and they dont have them every day, however it can also be caused by other high in fat seeds or generally occur naturally when the birds grow older.. it may sometimes be spotted by small black patches on the beak and i mean small, this is one of the late stages of the disease though and does not always occur
if the beak does continue to grow at a very high rate then a vet visit will be required ...
i suggest frit trees and willow brances as i know these are safe for the birds to chew, im not sure about pecan branches , their are some trees that are poisonous for the bird to eat so you have to be really careful, if you have a river or stream or pond around then usually you can find a willow tree, just snip a couple of thinish brances off every now and then,
i will find my list of poisonous plants and see if pecan tree is on the list and if not let yo know,
while apple branches are safe for the birds apple seeds are poisonous, so yo cant go on what sort of fruit you feed them to assume the brances are safe to as they are made from different things,
will do some searching for the list and let you know,
good luck with him or her, if it is vitimin shortage you could grind up the blockls so it gets the vitimins but you cant force the birds to chew unfortunatly

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best of luck
katie