What's wrong with an XOR? Logic is logic.
0-180 degrees, give or take a few off each end due to phase reversal (the transfer function goes up, then down, over the full circle), as determined by the timing constraints of the logic used.
I don't see that downconversion is necessary. Logic goes that fast, and I don't think you'll need ECL to do it. You can if you want -- after reading a few datasheets, you may find you need to. I don't know offhand.
If you want a more analog method, you can use a balanced mixer of any type, but mind that the input waveforms must be sharp and square to get a triangular (rather than sinusoidal) transfer function. Usually, one port (the LO, say) is driven with a high enough amplitude (from an impedance matched source) so that its signal effectively acts as a square wave current source/sink, switching the diodes quickly and solidly; the other signal is lower amplitude, so that it gets switched to the output alternately, without affecting the switching itself (as it would if it were the same high amplitude). So in this case, it must also be amplified, limited and clamped to yield a square wave, but at lower amplitude (say, two diodes back-to-back in parallel, before the signal enters the mixer).
Effectively, the convolution of the two waves is your transfer function; in radio, sin * sin = sin (read "*" as 'star' or 'convolved with') and sin * square = sin, so you normally don't need limiting on both ports; but to get a triangular transfer function, you need square * square.
Digital methods do the same, except you usually use a one-bit ADC (i.e., a comparator) to perform the limiting on both signals. It's all equivalent, as it should be.
The mixer method probably has much better noise floor due to using far less circuitry in the signal path, but you'll have to tweak and adjust and calibrate it to get known performance over the whole range.
As for the final step, just analog lowpass filter it. No need to count pulse widths, that would be silly. Let the physics handle it for you.
Tim