Combining two PWM outputs for finer granularity
The proposed circuitry solution is needlessly complex, and will not be economical to prototype or produce.   The entire premise of the question is not fully convincing, but accepting it at face value, there are far better ways.


As already proposed by user Dampmaskin, find a 16-bit timer.  Many MCUs have these, including not only the ATmega328p in either traditional or "Arduino" forms and also very low cost Arm Cortex M0 parts.
Alternately, implement PWM with larger count widths in software, either entirely or by using software to trigger a one-shot hardware PWM
Use one 8-bit timer in repeating mode to trigger another in one-shot mode.  This lets you effectively make much smaller fractions.  For example, if the repeat time fires at an interval of 10 milliseconds, but the on-time timer counts from a timebase of microseconds, your maximum on time would be 255 microseconds, but your repeat is 10000 microseconds, yielding a range of 0.01% to 2.55%.  When you need higher percentages, start reducing the repeat interval which functions as the divisor.  This can easily let your create on time percentages too low to have any response from a typical LED at all.


The advantage all of these have is that the output to the PWM power modulator is a signal from a single MCU pin.  At most, triggering one timer from another requires a single loopback wire or resistor from the output of one to the trigger input of another.