What to do when there's no more adjustment room on disc brakes
Ӎσᶎ's answer was the method I went with. I just got a washer from another hub (I didn't want to use a plain old steel washer from the hardware shop because I was concerned it might be too soft, though that might not be the case) and put it on the axle next to the cone. I did that In January and it's done about 4000k without any problems since then.