You are making your life very difficult with those requirements. I would suggest a stepup with 2 AA/AAA battery or a stepdown with the 14500 cell. It is easier with the 14500 if you dont want to charge it, with the two AA/AAA it is more user friendly.
The issue with complicated power systems is simple. You use two dozen components and complicated design, hard to source inductors. IMHO, inductors in the Bill of material are pain in the ass. And you spend all that time on the power system, instead of spending it on the application. Nobody will raise an eyebrow, if you need two batteries for it. You can even run the entire system on it, without any power management, if parts are selected for that.
Or use a coin cell, or oversized coin cell.