The buck regulator should provide some "filtering" and you may not need any further protection.
The way Zener protection works is it essentially "shorts out" when you go over the Zener voltage, and the fuse blows. In a signal circuit you can replace the fuse with a "current limiting" resistor, but in a power supply circuit you can't have a resistor in series.
A single Zener will clamp between (about) zero and +15V. Back-to-back Zeners will allow -15 to +15V (which you don't want).
The LC circuit is doing more harm than good... The inductor prevents current from instantly flowing... The spike appears across the inductor until it's magnetic field builds-up so the voltage is not across the Zeners and they don't kill the spike.
Once current starts flowing the capacitors start charging-up. With a long-term over-voltage, the capacitors will fully-charge and voltage will appear across the capacitors, so again the Zeners are not doing anything.