Aerodynamic Stability of Pellets

I would try to make the distance between the CG and the CP as large as possible. This would mean putting as much mass as possible in the pellet head and keeping the flare as light as possible. Of course if the flare walls are made too thin the risk of damage when in the tin and distortion on firing increase which is undesirable. It may be possible to change the shape of pellets to try to move the CP as far back as possible. The Sniper series of pellets may have evolved into a suitable shape for this, certainly many shooters found them accurate.

For heavier pellets, I would try to extend the pellet head rather than fill up the flare as most designs do currently. Filling the flare moves the CG backwards and increases the chances of spiralling, particularly at long ranges and high speeds. A big problem may be pellet length, though there is probably some room for development.
 
Been testing some pre-production .30 caliber Diablo 60 grain pellets. There very long tailed having a shallow divergent angle from the diablo waist.
Very head weight bias having a deep & somewhat thin skirt profile.

They fly quite well, but due to weight require quite the push to make the speed into the mid / upper 800's or better.

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I wonder if it would be advantageous to use a traditional lead aloy head and a lighter yet stronger skirt material, aluminum aloy perhaps. Allowing for thinner and stronger skirts,
As in ... Bi-Metalic

Or .. Perhaps made similar to the Hungarian SKENCO 2 material pellets having a metal front & plastic rear ?