The expanding glues are very useful for some things and they sure stick to wood. But you'd have to carve or sand off the excess after it expands on this job, and you aren't really needing the gap-filling advantage of the glue since the pieces will be lined up well and gaps will be very, very small.
Last time I used it (Elmer's Ultimate Glue or something like that) on the cracked plastic of the lid on my chest freezer it expanded and handled the repair amazingly well. But for a camera bed, why bother with it?
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