Dead drift works for things that aren't active swimmers. They tumble along looking for purchase. An emerging caddis fly, bouyed by gas and swimming to the surface is anything but dead.
Swinging should be quite valid for any caddis, as they're swimming to the top so as they go up the current moves them as well. Its a natural lifting motion, so the fly would take off from lower through the column and up to the surface. You're giving it a lifelike motion and triggering the instinct to take the fly before it escapes, which to me is why caddis rises are splashy affairs from below rather than sipping takes.
If you do, however, do not weight the leader, but weight the fly. When you weight the line, you'll create a pivot point at which everything beneath that point will swing much quicker, and more unnaturally. This would hold true in a cast of flies, where if you have one heavy fly at the bob followed by a lighter point fly the point will swing too quickly.