Pinecone with acrylic could be very tricky at that material thickness.
That is why I first mentioned that you did not specify the blank material.
That material was probably a bad choice for that pen in any case, just my humble opinion and not a criticism.
(13 mm final OD - 10.5 mm hole using the "correct" drill) leaves material thickness of 1.25mm = 0.050" ..... not too bad but a little marginal for a acrylic/pinecone blank from at least 2 points of view .... strength for turning/sanding and brass show through (which you can get around by painting to certain extent)
There is one other thing you can do to improve the wall thickness issue ...... a little teensy weensy bit ....
And that is to use a drill bit which is just a little tiny bit smaller than 10.5 mm
I don't remember what I have used for a Zen, but you can get away with a slightly smaller drill bit. . You would have to measure the brass tube with calipers and look up what drill size would come close to that, making sure to have enough clearance for gluing. . Secure gluing would be a very important issue given the "flaky" composition of some pinecone.
Mal, of course it has to be a hybrid.... Pinecone with acrylic. I do like your idea of turning a dowel then inserting that. Why does the material matter? It is for a Zen kit, the bushing size is .512 which is basically 13mm, so my 12.5mm hole theoretically leaves me with .5mm. is that enough?