I'm assuming you are keeping the lead casting inside the copper jacket, but did you not have the lead coming loose when it cooled down, due to contraction ?
I've been thinking of making similar ammo, but without the aluminium mould - simply pouring the lead into copper pipe-ends. The problem of shrinkage though - can it be solved by pre-heating the copper component ? - I don't know which metal expands the most upon heating.
If, fortuitously, it's the copper that expands the most, then by heating the copper to red-heat, then pouring the lead in, the copper enclosure would hopefully shrink down and grip that lead very tightly.