Had a chance to try the "tornado tube" coupling, and it does work great. I actually found that, once the flow was started, I could just start walking back toward my pack, carrying the whole thing in one hand, and gravity kept the flow going without any further squeezing or rolling.

The "scoop" I made by cutting the top off a Sawyer bottle also worked well. I used it on a couple of trips now, and have had no problems (I've been using the "new" Sawyer bottles, and they work fine; I may replace them with some Evernew bottles, though I'm not in any big hurry to do so.)