Fire damage to my bowsprit!
From my woodworking experience, the advice on the bowsprit is probably wrong, and the cracks are likely reapirable.
For the sprit, you''re going to have a tough time getting your 7 inch section to stay together if there''s only one joint. You''d still be dealing with wood in a ''timber'' format, which is going to have some very powerful differential movement. Either go with a single hand selected stick or multiple smaller laminations, on the order of size of a commercial ''glue lam'' beam or smaller.
For the box section mast, it shouldn''t be too tough to kerf the full depth of each joint along its length. If the mast is built with rabbeted side cheeks, the joint at the bottom should keep the mast together, other wise do the kerfing in segments to keep the pieces attached. Wet the kerf with ''neat'' epoxy, and then fill it with fiber-strand reinforced epoxy. For appearance, re-kerf the joint to a very shallow depth and glue in matching-species splines to cover the epoxy kerfs. All this assumes you''ll get the mast on the ground, of course...