I don't believe the shape of the bearing edge would have any effect on how well the drum holds its tuning. After all, the only things that can cause the pitch to drop are skin slip, stretch in the rope, or stretch in the skin (or a combination thereof).
I honestly can't see how the bearing edge would cause what you describe. Just maybe (but only just), with a really sharp bearing edge, there is less surface area where the skin is stretched over the rim, reducing the amount of static friction. But that's a theory only…
Suggestion: if you don't like the bearing edge anyway, reshape it to something more reasonable next time you replace a skin. And, while you are at it, use the double-hitch loops shown in
this post. The additional contact points will almost certainly eliminate skin slip. If the drum then still won't hold its tuning, it would have to be the skin or the rope.
Cheers,
Michi.