If you want to attempt a modification, you could try a trick I learned from Kurt Hertzog.
There's a type of wood glue that expands (or "foams up") as it cures, here in the US one brand is "Gorilla" polyurethane glue. The foaming action happens when it comes into contact with water, it fills gaps in a wood joint, then cures hard.
Get a tiny drop of this glue on the tip of a toothpick, and reach inside the cap to deposit the drop on the internal threads some way up. Add a drop of water to the threads on the pen, and screw them together tight. Wait however long the label on the bottle of glue says it takes to cure, and then unscrew the cap - you'll have to twist hard to break the glue bond, but since you only used a tiny spot it won't be impossible.
Clean up any glue in the threads of the pen - toothbrush, Brasso, dental floss - whatever your standard technique for cleaning up threads is.
The glue that's left inside the cap will hopefully add enough grip to keep it from unscrewing.
