I have drawn down winchester power point bullets made for the .303 in a lee size die made for the .308, no problem and they shot OK in my .308.
I think your project would turn out Ok if you chose cup and core bullets originally in no more than .323" diameter, pushed through an appropriate Lee size die. One tip that I have read about, the first pass might not be quite enough if your draw die is exactly the bore diameter that you require. There is a small amount of spring back in the bullet. My .312" bullets measured .3085" when I was done one pass, good enough.
Actually, .318" diameter bullets made for older 8mm rifles might work just fine if you are careful working up loads. 2 thou is not a greatly oversized bullet if you keep pressures reasonable. Good luck!