Disable the PWM and set the PIN for the LED high instead (one option)
Alternatively, you could use the inverted output from the PWM and invert all of your duty cycle values; That way, the default "reset" state is ON rather than OFF, but then you will run into the same issue for a 0% duty cycle.
If you increase the period, the pulse will become relatively smaller in comparison, and thus less overall effect.
(Just some thoughts, but I don't know of any really good fix for this)
If you're incrementing the pwm compare in an ISR you can stop the interrupt and you wouldn't have the reset issue.
Stopping the PWM and then restarting it will cause a visible brightness glitch.