You need enough of an unrectified load on the SSR for it to see a full AC waveform. It would *probably* work if you added an 18K 1W resistor from the SSR switched Live output to Neutral, unless the SSR requires a minimum load current >6.6mA.
However for the reasons other posters have listed above, diodes to reduce the power of a high current load are a dumb idea that can get you in trouble with your electricity supply company, so I wouldn't recommend leaving the diodes for half power in there.
If you are implementing cycle skipping control, you need a line frequency reference to your control circuit so you can avoid skipping half cycles, and only skip whole cycles, also to avoid DC imbalance. One approach is to use the line frequency input to clock the PWM through a D type flipflop before feeding it to the control terminals of your zero crossing switching SSR.
You can derive a suitable line frequency signal by tapping one of the AC outputs from the transformer to the bridge rectifier of a conventional linear PSU, and feeding it through a resistor with a Zener clamp (to 0V) to reduce it to your desired logic level. That gives you a somewhat assymetric line frequency near squarewave, with fairly poor rise and fall times. Clean it up with a Schmitt trigger input buffer before you do anything else with it.