The trash always floats to the surface. What you do by fluxing with beeswax- stir the lead while the beeswax is melting and burning off, is to draw small impurities to the surface so they can be SKIMMED OFF!
I learned this all the hard way when melting lead we dug out of dirt backstops at ranges. The lead came with lots of dirt and other impurities. We were making pistol bullets, so the alloy didn't matter all that much. However, the stuff was very difficult to clean, and we found we had to first pour it into our ingot mold, after stirring, fluxing a couple of times, and then skimming repeatedly as stuff came to the surface. Then after it was in ingot form, we could add it to the lead pot and melt it down again, and more small stuff would float to the surface. You could tell the difference when you were sizing the bullets, as you would occasionally hit some impurity that would make it through and give added resistance to the sizer. We learned it paid to find lead sheeting from roofers, and other sources of pure lead if we wanted clean lead in the pot. That didn't stop us from picking up lead from the back stop, but we did the extra steps to clean that lead, and mixed it with pure lead to bring the amount of tin and animony down. Years later, I found that its the antimony that makes the lead so hard and brittle, not the tin.