While waiting for my 10F PICs I had a little time today and did some experiments with a PIC12F683.
Using the internal oscillator set for 4MHz and a close loop with Toggle GPIO.x I was getting in the neighborhood of 70 kHz output and 143 kHz for 8 MHz clock.
Interestingly enough with simple High / Low GPIO.x loop I got about 200 kHz.

Then I realized that one of the clock options is to use internal clock with clock/4 on clock out pin. This method got me the 1 MHz output for the 4 MHz internal clock and 2 MHz for the 8 MHz internal clock.

The oscilloscope shows a pretty steady output and my frequency counter gives about 0.15% error.

If this will prove to be my path I will use a one gate chip to buffer and modulate the output.

I still wish I will be able to solve it with only one PIC10F and I will try my best to find a solution.

Nick