After toying around with different ideas (including getting an off-cut of birch and just drilling a hole in it) - I came up with a basic idea:
(Above: Not terribly elegant, but it could work)
After showing my girlfriend the general idea, she seemed to like it so I went ahead and started construction. However, I made a few modifications to the original design. (More specifically, I totally redesigned it)
I had a tiny bit of scrap Baltic birch plywood left over, and some 5/8" dowel that I ended up buying and not using for another build. So with that I cut off some of the dowel, trimmed up the plywood, and drilled some holes.
(Above: Can you guess where this is going?)
I drilled through one of the dowels, and partially drilled into the second dowel - which would allow the trinket to slip through one piece of dowel, and be cradled by the lower piece of dowel.
I then countersunk the holes I made in the plywood for the dowels, and the holes I made for the mounting screws. A small application of wood glue to the backs of the dowels, and a couple #6 screws later - the dowels were secure. To make sure everything lined up, I slipped a stirrer through the holes in the dowels.
Some light sanding, and a test fit and the holder looked like it would do the trick.
As a side note - the whole 'laser print / acetone label transfer' thing I've seen on Youtube - did not work for me.
Upon visiting my girlfriends place, she decided where she wanted it to hang, without her cat being able to get at it, but a place she could see it. A couple of wood screws later - here we are!
And in case you were wondering, the trinket in question is a handmade glass stalk of wheat. I left it unfinished - I like the way the raw wood looks.
Thanks for reading!