Best way is to go with common mode choke if it´s a must.
You should put a schottky between the regulator and the inductor and from the other side connected
to the ground and pointing to the first connection.
You should use dampening, rule of thumb, parallel to your existing capacitor you connect a snubber circuit,
snubber capacitor 10 x the filter cap and a resistor equal to the minimum impedance of the filter at resonance.
You will be much better off to just use a regulator with less noise and / or depending on what you need better CMRR figure.
If not go for a RC, which yeah I know it´s going to be big on the PCB but, LC is really overkill.
Regards,
Lefteris