1 - When you ask technical questions, it is VERY helpful to tell people what kind of rifle(s) you are talking about... I'm just saying.
There is nothing in your post that is unusual, or suggests the need for a custom die (which you will NOT be able to get for the 223 x 40° improved.... no one makes them). Custom FL dies are only made for 4 or 5 calibers - the BR family, the PPC family, the 6mx47, and maybe one or two others... the ones used in benchrest shooting.
The amount of resistance of a die is due to the size difference between the chamber and die - if you have a loose (maximum) chamber and a minimum FL die, then you will move the case walls more than if you have a minimum chamber. If you have a large or max chamber, there is nothing you can do (short of a new barrel and min reamer).
Your 6mmBR is very likely a minimum-ish chamber and the die has very little work to do. Your 223 improved is likely a max or large-ish chamber and the die has more work to do... and there is nothing you can do about it. As you gain experience in reloading, you will find that ALL dies in different calibers will feel different.
That is the only difference between the two - you don't have a problem, except worrying too much about nothing.