Frequency division and signal spectrum
I would observe that your two tones can alternately be seen as a DSB modulated carrier at the average frequency, 100% modulated by half the difference. 

$$\cos (\theta) + \cos (\phi) = 2 \cos ((\theta+\phi)/2) \cos ((\theta-\phi)/2)$$

But your clipper effectively converts the phase modulation component to pulse width modulation (this is much more obvious if you re run the maths with the carriers much further apart, try a 50kHz spacing) in a horribly non linear way, kind of like jitter on a clock, I think there be bessel functions hiding in there somewhere. 

The divide by two however is an edge triggered event but the place the edges really move a lot is right around the modulation zero as the difference component swaps polarity and you will usually get an extra edge at this point, giving you the single tone (The divider does not care about width, only either rising or falling edges) with phase discontinuities at the difference frequency as the $$\cos((\theta-\phi)/2)$$ term changes sign.

Possibly a bit handwavy, but it has been a long time since school.