If you try this, you might want to turn your plane blade over, with the bevel up, as it will not be so prone to grab the quill, and have the most minimal blade exposure as possible, and still be able to cut.
And be sure the blade is "SCARY SHARP" !!
But how are you going to clamp the feather, and not plane the clamp?
If you have a block plane, you could put side rails on a jig, but that is a lot of trouble, when you could just use a sanding block.
Just my most humble opinion, but by all means try it, and let us know the results, could be something new to do, or...... not to do. We learn by trying, and by looking at others mistakes, as the old poster used to say,...... "Behold the turtle, he makes no progress, till he sticks his neck out.
Wayne