I do not think there is a better powder than Lil'gun for the 22 Hornet. They developed it for 410 shotgun, but it feels like they developed it for the Hornet. It also made the 17 HMR into a reality.
Speer #14 manual - "For this manual, we used CCI small pistol primers instead of rifle primers. This change allowed higher velocities at safe pressures, and greatly reduced the extreme variation of pressure that limited the number of propellants we showed in previous books." They went on to say they tested them in different action types including break-open actions. They said if you have any trouble with primer flowback - then there is too much clearance between the firing pin and the breech face or the firing pin is weak. In either case it should be corrected with a gunsmith. They also warned that using their loads with rifle primers would increase pressure above 22 Hornet safe levels.
For 40 grain bullets Lil'gun velocity topped out at 3020fps, the next highest was WW296 @ 2782 fps. With 45 grains bullets, 2913 for Lil'gun and 2619 for WW296. You can see a significant difference between Lil'gun and it nearest competitor. 2900 fps with a 45 grain bullet isn't too shabby. Curiously the 33 TNT only developed 73 fps more velocity than a 40 grain bullet. It fell behind H110, 296 and AA No.9 with the 33 grain TNT. It may have something to do with case capacity, they are showing 14.0 grains of Lil'gun compressed, I do not think you could get any more in there.