Kate,
I've found that the chaff doesn't make any difference in terms of germinating the seed. If you put the whole seed stalk into a paper bag and keep it dry and cool most of the seed will come out and collect at the bottom of the bag. After I collect that very clean seed I generally put the stalk back in the bag and give the stalk a little squeeze. That releases some of the seeds that are still entrapped in the capsules. This releases the seed but also creates much more debris. However, if you dump that debris/ seed mix out on a sheet of white paper you can sort of manually separate the larger pieces of debris from the seeds.
In November I find that all the seed is ready to come out of the capsules and so I generally wait until then to do a cleaning and I store the seed in the CRISPER portion of my refrigerator in glassine envelopes. I plant the seed in late February or early March.
Good luck with the seeds!
Kevin