I would be careful with a diode drop in your design. Under load it may drop too much that you want to use a Schottky diode, but in sleep a Schottky diode may only drop 100-200mV at 10uA (often not specified in datasheets), which then increases the supply voltage again.
An active regulator of somekind would do better.. Not sure if it needs to be buck-boost. You could perhaps also use a buck converter and run your whole design at e.g. 2.7V or another low voltage, such that the converter has enough headroom at the lowest battery voltage you need to support.
I wouldn't let a microcontroller run at elevated voltages all day.
Or in extreme cases for short periods. At a previous job I've seen a fault of a production test jig, that put 12V briefly (like 2s at most) on the internal 3.3V of the product during programming. Complaint was: the devices wouldn't program. I fixed the jig, but the devices used to diagnose the problem were scrapped. In that case a failure of such a device could lead to a road accident, so no chances taken.