Since you are re-inventing the wheel instead of swaging bullets.........
Ok, if "I" were gonna do this :
1. Find a way to size the case "right". Using a 375 H+H expander ball and lube- the full length of the case sounds like a decent start to me. ( since you are gonna snip the tip, and make it the right length for a projectile anyway) This will give you a tube- not a wonky cylindrical pyramid. Well, a heck of a lot more of a tube than you started with. IF that doesn't do it- Find a decent cheap drill bit thats the right diameter, and go real slow after dulling the cutting edges.
2. Find something you can slip the case into, that will allow you to fill the brass over the top with hot lead, and remove it once cooled- like a bullet mould. You want at least 1/4".
You could probably use heat shield tape, but it would be labor intensive. Given what we're looking at though....... While we're on heat- bake that case real good, and make sure its soft.
3. Use that top head of lead you have, and a file, and make something more aerodynamic than a flat SWC which you'd get from a flat case top.
You could trim the case shorter, and add more "top" to make a pointy bullet, if you wanted.
I agree with sheep- Its doable, and men have done far better with much less. Experimentation is the core of our passion.
Unless its something Rediculous like "I wanna make 6 powder salad, what would you use" or " whats the best way to make mercury tipped bullet proof vest penetrating exploding hollowpoints" I don't see the point of ridicule.
I say do it- and keep us posted.
The way things are going, we're going to be recycling bullet jackets soon, and people are going to be forming copper pipe from the downstairs bathroom no one uses into bullet jackets using self-drilled swaging dies and a hammer.
ReloaderFred is gonna be answering a lot of questions- lets put it that way.