The code is now up. There are three new functions and an example sketch to explain how they work.
To be consistent with analogWrite(), pwmWrite() will always perform 8 bit pwm. If a higher resolution is necessary, use pwmWriteHR() instead.
void pwmWrite(uint8_t pin, uint8_t duty) 8-bit, 0 - 255
void pwmWriteHR(uint8_t pin, uint16_t duty) 16-bit, 0 - 65535
Unfortunately, resolution control is not that simple once custom frequencies come into play. If you modify the frequency on a timer, the resolution will change. The general rule of thumb is that the higher the frequency the lower the resolution. There are several variables that the SetFrequency functions wrap. They are aware of them and will mathematically determine the highest possible resolution at that given frequency. Although pwmWriteHR() accepts a 16 bit integer, it will automatically map to any timer resolution. To know whether the resolution is too low for your tolerances at a particular frequency, I have added two functions.
float GetPinResolution(uint8_t pin)
float TimerX_GetResolution() (replace X with a timer number)
These functions find the resolution in base 2/the number bits required to represent the resolution. Please note that both return floats, not ints; that is intentional. If you prefer to find the number of possible values instead of messing with binary, use TimerX_GetTop() and add 1 (which is the same thing but in base 10).
I added a sketch called PWM_lib_resolution_example to the project to demonstrate these functions and the relationship between timer frequency and resolution.
I have not been able to find enough time to exhaustively check this code for bugs, so if you find any please speak up.