The fact that the ingots were shiny tells you that they contain significant amounts of something other than lead. Pure lead corrodes in minutes, it is quite a reactive metal, like aluminium. The layer of corrosion prevents further corrosion, a bit like a layer of paint, stopping the oxygen getting to the metal.
http://www.tackleunderground.com/forum/wire-baits/14776-looks-like-lead-but-doesnt-act-like-what.html this was a recent post on a similar problem. Didn't really get resolved here, but worth reading for comparison.
Of the four common metal elements alloyed with lead (tin, zinc, antimony and bismuth), two have melting points higher than lead (621F), these are zinc (786F) and antimony (1166F). So your residue is probably one of these. If you heat the lead up more and the problem does not go away, then it is the antimony.
I'm not so sure that the metals are supposed to separate like this (edit, Dano thinking the same), I thought that the melting point was altered. Maybe the original melt was not mixed in sufficiently, just theorising (guessing).
If more heating does not solve the problem, then just skim it off.
Here is the link to that thread on fluxing: http://www.tackleunderground.com/forum/wire-baits/13893-best-lead-melt-flux.html it contains 7 pages of quality, useful information about alloys, thanks to Sagacious.
The important thing is to report back when you find the solution, so we can all learn some.
Dave