You do not, methinks, want to go pulling that bushing out until you see what it is that's holding it in--if you splinter the wood, you are in a bad prediciment. It seems to me that if it will not just come out; and it is rotating; then there is something that is keeping it in place under the veneer (if there is some on your camera)--my mushroom analogy.
Once you get it out without damaging the wood, then you have options; and easy ones, I should think.
I used one of those quarter inch whatever they are called to mount a homemade wooden platform to hold my Ansco View Camera on a tripod at the center of gravity. It simply required countersinking the 1/4 inch hole wide enough to encompass the flange part; and just deep enough so that it does not impinge upon the tripod head. Epoxy did the rest.