The highest probability is that the switching power supply inside the LED lamp unit is making all kinds of radio frequency noise. Since that RF noise source is very close to the radio and its antenna the poor radio is getting overwhelmed by the noise.
Since you've already tried ferrites there are only a few other options available to you befor the most obvious option can be exercised. That obvious option is replacement of the LED lamp modules with quiet ones. When buying cheap Chinese LED's it's hit-or-miss. Shell out some cash and buy a set of good lights (Baja Designs or Rigid) and you won't have the noise to deal with.
If you still want to mess around with these lights, buy some shielded cable for the power leads. Don't ground the lights locally but rather run 2-wire twisted shielded cable. Tie the shield to the chassis of the LED lamp modules. Back at your power source tie the power ground to a single common ground point and ground the shield to this single common ground point. See if this helps. If it doesn't unfasten the connection between the shield and the chassis of the LED lamp modules and see if it's any better.
Another option is to buy a torroid core and near the LED lamp modules loop the power and ground wires around the torroid several times before running back to the power source and common ground.
Again, I'll suggest sometimes the easier way to deal with cheap lights is to donate them to somebody you don't like very much and then buy better lights.
For what it's worth, my Baja Squadron Pro lights are absolutely silent on the radio and they are mounted within inches of the antenna.
