I had been using the "lightly sprinkle...barely tamp" version of the "Three Levels" method. It seems that when the tobacco was sprinkled very lightly and the tamping was also very light, the pipe would smoke too "loose" and was going out almost constantly, especially with English blends.
To correct this problem I started "feeding" the tobacco into the pipe while it was tilted sideways in one hand. This seemed to take the pressure off the airhole so the airflow was not obstructed yet there was less space between the tobacco strands. This manner of packing seemed to keep the strands more consistent for keeping lit on it's own better. I also pressed the levels down a bit harder but not "too" hard as to "mash" it down.
In the end, the pipe seemed to be borderline overpacked. The initial light was a bit tighter than I like but it was working well. After the first char then second light I took a pipe cleaner and gently went down the stem and gave the tobacco load a little push. This cleared the airway in the chamber and opened up the draw to a perfect tension. The result was a good long smoke with fewer relights, a better flavor and slower cadence.
This method is far from foolproof but so far it is working well. Give it a try and let us know how it works for you!