Before I had the tools to make my own dies, I would modify store-bought dies by lapping them.
I'd start with a die at least 0.001" undersize, preferably 0.002" undersize. Even though I tried to lap only the entrance, it was impossible to avoid lapping the rest of the die at least a little bit. Plus, storebought dies are usually out-of-round and have burrs, anyway, so they benefit from light lapping.
Make a bit to hold a piece of emory cloth in a drill chuck. Just hacksaw down the middle of a piece of say, 1/4" round rod, far enough to hold a piece of emory. Now wrap the emory around the bit and have at it with the drill. A 1/4" die grinder might work even better. Try to stay at, and just inside, the entrance of the die.
The emory will quickly dull, so you'll either have to keep replacing it, or else freshen it up with valve lapping compound.
The process is very slow, typically taking 30 - 60 minutes.
Alternatively, you might be able to use a tapered carbide burr, with everything securely held in a drill press. But carbide burrs are expensive, and the finish tends to chatter, so it would still need to be cleaned up by lapping.