Would I need a zero-crossing SSR for a reflow oven controller?
The oven itself won't care where in the power cycle the heater is switched on and off.  The time constant of the heater should be many times the period of a power line cycle, so timing details at the level of power line cycles don't matter.

However, the rest of the world might care.  Switching at the zero crossings reduces the voltage and current transients.  That in turn reduces conducted and emitted interference.

If I were doing this, I'd try to switch at the zero crossings.  If this is a commercial product, you may need to switch at the zero crossings to pass EMI (electromagnetic interference) requirements.