There have been various threads in the past about working with down. I haven't used a tent myself and would be leery of it because of the static electricity interactions between the down and the tent and sleeping bag fabrics.

What I did was clear and clean up about 6-8 m2 of space on a carpet and work slowly so that the loose down settles and gets caught on the carpet (and on the down that's already on the carpet) as opposed to flying all over the room. Once you're just about finished, you can collect the down from the carpet (and from your clothes, hair, etc.) with a vacuum cleaner hose covered with a couple of layers of no-see-um (pick off the compressed down from the netting frequently if you don't want to fry the vacuum cleaner).

Stephane