For eliminating common more conducted interference, you should try and deal with it at the source. Usually the source of such interference is some node with high voltage and high frequency signals, which is coupling directly to other parts of the system (including the chassis/frame of the car) via electric fields (capacitive coupling, basically). Even though it's still happening via coupled fields, it's still conducted interference, so your second battery experiment doesn't disprove it. So what you would want to do is prevent all that electric field from reaching anything other than your local circuit ground. Generally this is done with a faraday screen or shield surrounding the problematic nodes, and you attach that shield directly to your local circuit ground. This allows those currents to flow, but in a small, controlled loop which doesn't interfere with other systems.
If that problematic node is in the lamp itself, then it may be an issue of mounting the lamp differently. Hard to tell without seeing its construction in detail.
For differential mode interference, you should be able to get away with just using high quality snubbing capacitors. Look for polypropylene metalized caps, like the MKP types from Vishay or EPCOS. You will likely need several uF total, placed very close to the ballast, in order for them to be effective. Even if 100nF at 50MHz is very small, there may also be additional impedance in the form of ESR and ESL (parasitic series resistance and inductance) that completely dominates that. So use bigger caps, with very short wires. If you do things properly, it's likely you can get away with no chokes at all.