Nice bird!
I used to split my cedar birds with a hatchet to get the two halves. Then they have a LOT to grip, and only have one way to slide. You just have to let 'er rip and not look back once the hammer drops! Hesitation will lead to a bad split. Also read the grain first. Then i'd use TIII. Now, i cannot find any cedar and am using tupelo. Tupelo will swallow a hatchet. I use a saw to cut the birds in half. I have this resin for boats from the boat shop, and i drill 1/8 (or what ever you have nearby) in holes in each cavity where they'll join. I then apply the resin to both sides, and press togather with my hands and position them. NO CLAMPS, you don't clamp epoxy or resin too often. Since the saw takes wood OFF the bird that the hatchet would NOT, the resin will act as a glue, and filler. Look at old boats that were built with resin, the old timers swore by that stuff. It is great. The best thing is if you try to clamp the two halves that you carved, and then cut out material with the bandsaw, then you will have to recarve the seam to get the two halves to fit (since they were not carved to have a gap cut out with the saw.) The other alternative is just to take two pieces of wood, cut out your pattern, and carve them as one bird (screw them togather) then when you're ready to hollow, unscrew it and you have a seam that you "carved to" (or will have no material taken out that will change the seam/transition between the halves.)
Hope this helps!
Spencer