In the opening question, you refer to a "picked" bullet as the projectile in question. Ned Roberts in his timeless tome "The Muzzleloading Caplock Rifle" refers to conicals as "picket" bullets or "sugar loaf" bullets. I'm not trying to be a nit-picker or anything, but I suspect that's what you were referring to. I haven't ever read about their historic use in the Walker, but I suspect that it would have been a bit risky putting a bullet weighing perhaps twice as much in a gun which was well known for it's propensity to blow up with round balls over maximum loads. (Of course the conical would have used more room, making for lower powder charges, still...) Just a thought. On the other hand, maybe that's part of the reason for the ones that DID blow up?
Jamie