Don't ever poke the stick deeper than halfway to the bottom. Use an SS teaspoon for scratching around below that.
Or better yet don't use a wood stick at all. When that became a big topic over on CB I tried it with paint stir sticks. I tried it once, never again. The melt is plenty hot enough to char the stick, it won't burn because there is no air under the melt but it does char and bits of charred wood do break off and they do become trapped by the density of the lead. They will end up in your ladle or in the spout when bottom pouring.
Proper fluxing is not trying to force anything below the surface of the melt, not a stick and not sawdust. Proper fluxing is bringing the alloy up and pouring it through the sawdust.