Jimetal's way is the quickest I know of. His method takes you directly to the traders rather than the collection summary where you have to single out the traders.
If ever Admin implemented a function to move cards by team, it would speed things up drastically. There will always be thousands of sets and players, but only a few teams. Maybe that's something he is working on.
I'm going to reevaluate how I collect after the new year. It's just getting way too expensive for the new stuff. Sometimes I just want to buy a pack, not a whole box or even blaster.