Yes, deeper is easier. At 10 meters, it will take half the number of breaths that it takes at the surface. It will only be half full when you release, but the expansion will fill it out on the way up. If you cut your spool down to 15 m, you probably shouldn't deploy from deeper than about 10 m to allow for the angle due to current.
If you really want quick, you can use your BC inflator hose on the oral valve. Less than 2 seconds, and it pulls HARD. If you're tangled, you're going for a ride. I wouldn't suggest doing this for the first time in open water.