Although I have made many pens, I have never made a pine cone pen. I have seen an acquaintance make one though. He did not stabilize the cone. In fact, he stripped it down to the core. He commented that he likes pine cones that squirrels have cleaned for him. Cut the core into two parts, measured and cut for lengths, drilled out and turned TBC. Used a bit of CA on some soft spots, laquer sanding sealer and laquer finish.
I did not care for the appearance with the cone spots but it finished nicely and no problems just using the pine core.