Programming the for PWM for 60hz and getting a 7.5% duty cycle.

Firstly pins 10 and 11 run from two different timers - pin 11 uses timer2 which is 8 bit and can only go down to 61.03Hz minimum at 16MHz system clock - is that satisfactory?

You might do best to use two pins on the same timer, so pins 9 and 10 (timer1), or pins 11 and 3 (timer2).
You'll have to reset the timer's prescaler value to clock slower than the default, then choose an appropriate mode - for timer1 mode 8 (phase and frequency correct, period set by ICR1) would allow two PWM pins to work.

I think with timer2 there is no way to set a frequency-correct mode and have both PWM pins work, but since you are limited to 61.03Hz, frequency correct is already a lost cause. If 61.03Hz is OK, then you probably just need to change the prescaler bits and use analogWrite() on pins 11 and 3:

Try

void setup ()
{
  pinMode (11, OUTPUT) ;
  pinMode (3, OUTPUT) ;
  TCCR2A = 0xA3 ;
  TCCR2B = 0x07 ;
  analogWrite (11, 19) ;
  analogWrite (3, 19) ;
}

and see if the right sort of signal comes out