Make your join before you finish the shaping. That way you guarantee centre. Finding centre is easy tho if you understand mathematics. If you have a circle end; measure the longest line you can internally. Do this at several points. Where they cross is the centre. But yeah; this will fail, woodworking was correct. First real impact and you will have two short sticks with a screw in one end of one of them and a shattered end on the other.