I agree. While the others advocating tin are not wrong, I just don't see that as a real fix. I cast a wide variety of alloys including pure lead. All alloys, or pure lead can be cast to complete satisfaction if your technique is good. Tin does help reduce surface tension which does seem to make fill out easier, but it still wont overcome more than a minor problem.
Sprue plate temp is a factor for the base of the bullets, but I've not seen it effect the rest of the bullet. It is worth noting that I have seen sprue plate temp cause issues of only one side of a bullet base filling out, however, the rest of the bullet is filled out well. That is generally from too cold a sprue plate which solidifies the lead in that spot before the other side. To combat that, I often alternate which end of the mold I start pouring into each cycle.
I would still be looking at fill rate or venting first. You say that it is already filling so fast that lead would splash out if you went any faster. That could indicate your mold is not venting well. It could also indicate you happen to have a pot that can flow a lot faster than most. It's really hard to critique your method without being there. A picture would help us a lot.