Varget will reduce to that level fine, but your issue is still possibly with fit and hardness.
Make sure the bullet just barely fits (trying to size JUST the nose can/ does bend the bullet and I don't agree with Veral) and make it as hard as possible. A BHN of 25+ will not be out of line.
If you need to get a .365 die to get a .3665-.367 diameter bullet to fit, do it and size the whole bullet, NOT just the nose and make sure the bullet is sized even.
I've sized rifle bullets longer than yours down .005 (375gr. .418 bullet to fit .412 throat, .411 groove) with minute of angle accuracy and have ran LBT's in ten bottleneck chamberings, most at jacketed speeds, some needed Dacron to maintain accuract, but I've never seen any shoot worse than 3 inches at a hundred yards! Ouch!
I really hope you can get rewarded for going through all of this.
