Trapezus, one of the things that the U.S. Navy Underwater Swimmers School instructors did was to ensure that during our earliest days with the double hose regulator (U.S. Divers Company Aquamaster) we dove without non-return valves in the mouthpiece. This ensured that we knew how to clear the hoses when water was introduced, and without the non-return valves. I recently got a La Spiro Professional Mouthpiece that European and Cousteau divers used, and it has no non-return valves too.
So one double hose skill I would insert is to be able to clear the breathing tubes from a completely flooded condition without non-return valves in the mouthpiece. To do this in a ditch-and-don, first ditch the scuba, and allow the breathing tubes to fill with water totally. This means shutting off the air, and not placing the mouthpiece under the valve (which traps air in the hoses). Then dive down, turn on the air, pump the hoses to initiate flow, and get a free flow going. Then put it in your mouth and clear the exhaust hose. From there, the unit can be donned if the diver is behind the unit (allowing it to go up over the head, with arms through the shoulder straps) and be positioned in dive position.
To clear the hoses in the dive position once the mouthpiece is removed, you need to do the roll maneuver that is shown in The New Science of Skin and Scuba Diving.
This will give a good appreciation for those little mushroom valves in the mouthpiece.
We sneaked non-returns into our mouthpieces prior to our deep open water dives in the U.S. Navy Underwater Swimmers School checkout dives in the last week of diving.
The other thing to add would be the importance of positioning for the double hose regulator.
Note the regulator being low, between the shoulder blades. I have a book which shows this difference pretty well, and will post information about that soon.
SeaRat