ammunition, ammunition-reloading, castingThis is a two part question:
It’s hard to find a non-lead material that works reasonably. You could use a bismuth based alloy (low melting point) but the cost would be exorbitant. Brass and other cuprous alloys are much harder to melt and the equipment to do so is outside of what most people would find reasonable for bullet manufacturing. Tungsten ‘inserts’ would be illegal to manufacture in pistol ammo.
Any type of insert poses an additional complication as well and that is maintaining a concentric center-of-gravity. At best the bullet will precess resulting in high drag and a low ballistic coefficient. At worse it may not even be able to stabilize.
If you have those issues handled, keeping the ‘inserts’ on a metal tray attached to the melting pot should heat them sufficiently, but you may have the opposite problem - that the bullets take longer to cool.
The manufacture of bullets with multiple materials is normally done by swaging, which cold-forms the malleable metals under terrific pressure. The center-of-gravity issue would likely be handled by first swaging the soft (lead) core with an imprint (hole) for the insert. The insert would be placed in the hole, capped with a jacket blank and then swaged to final form.
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