There are a lot of factors. If you're really set on it, take it to a very qualified tech/luthier and see what they think.
its an extensive task but a decent luthier should be able to work with what you have. Ive seen some really thick boards, so you do have some wood to work with, but if you are that unhappy with the birds, why not consider purchasing a brand new board with the inlay choice that you want, and then have the board replaced?