Egg Pickler here and can confirm. As for shelf stability I will tell you about a jar of eggs found in my cupboard marked only with month. We lived in the house for eight years by that time.
They were so picked that the yolk and white were indistinguishable in color. The texture was like a rubber bouncy ball. One did bounce nicely when gently thrown into the sink. Egg was still edible and did not make me ill. The jar was not sealed. Those had been opened for years.
As for quail eggs I was taught to agitate them with chop sticks while boiling.
Yes, agitating is important to keep the yolks centered. There's also the matter of a thicker membrane than chicken eggs.
(post is archived)