Make a barrel lap
Take a 4"-5" length of 3/8 steel tubing and pinch it oval about 1" from one end.
Pinch it oval and try putting the .400" die over it.
You are looking to get the tube oval enough to just slip thru the die with some resistance.
Chuck the tube in either a hand drill or drill press, smear some lapping compound on it and lap the die.
My 1st choice is always using a drill press and the item being lapped can be hand held and allowed to float around with the oval/wobbly lap but not spin.
If all you have is a drill, clamp in a vise and hand hold the part being lapped.
The tube will wear but you only need to re-squeeze it, making it bigger, and continue to lap the .400" die until it measures .401".
Done right and you will end up with a true round hole without any taper.
This will be way more affective than anything mentioned in this thread and is true "lapping", not just polishing with paper and calling it honing/lapping.
You can also make a lap from tubing by cutting/hacksawing an upside down "L" cut into the tube end, and bend out the resulting tab until it fits thru the die with some resistance and lap the hole with that.
edit: vise grips are great for the oval pinching because of their positive stop and can be precisely adjusted.