.....I assume you glue everything up before you turn and hollow....
Jonathan, I turn, glue and bore out as I go.
Start with a recessed dovetail base (fully finished on base),
rough turn and clean up one face of the other pieces, making very sure that the glue interface is flat (squeaky steel rule trick).
Mount base on chuck jaws, face off front face, bore to required depth if deeper section, clean up edge square, (squeaky steel rule trick again).
Glue on next section, use tail stock to apply pressure.
Finish bore to match base, sand and finish, trim outer close to base dia.
Square off front edge (squeaky steel rule trick again).
Glue next section etc.
Finally finish outer.
Finishing the bore as you go is easier for tooling and finishing.