My maths (which is often faulty) tells me that at 500Hz a cycle takes 2000 µsecs. As analogWrite() takes values from 0 to 255 the granularity will be about 7.84µsecs. That suggests that 135 gives 1060 and 240 gives 1881.

However the control would be very coarse - just 240 - 135 = 105 steps between min and max. Doesn't that negate the purpose of the high refresh rate? Using Servo.writeMicroseconds() you would have 821 steps over the full range.

...R