I really don't know what you use for a wood filler, so I may be out of line here, so if I am wrong then please correct me. I am not a fan of using commercial wood fillers due to the ingredients they contain. Most of them use such chemicals as acetone or acetate as a solvent and/ or use plastic fibers or granules as the primary filler material and I am really not confident in how safe they are for the birds. I do see how these materials could discourage the bird from continuing to chew in that area though.
Although it does not produce as smooth of a surface without a bit of sanding to it the only filler that I use where my birds chew is made at home using only a fine sawdust ( the finer the better) and Elmer's white or wood glue as that is the safest glue that I have been able to find for this purpose. If you are lucky enough you might be able to find some hide glue like the kind that used to be used for restoring some antique furniture.