twistedtree
Guru
I would be looking at the wire runs from the lights and the proximity of the coax cable from the AIS antenna. If the coax cable is close or bundled with the running light wiring you should separate the wire runs to the lights from the AIS cable. There could be problems with the shielding grounds on the coax to the AIS antenna. There needs to be a proper low resistance bond at each connection and then to the vessel ground to the antenna housing. Also it would help if the running light/anchor light were twisted pairs to help reduce emi interference or a shielded twisted pair. Check out the runs as it seems to more of a problem than the light bulbs.
I think before chasing and adjusting cable runs, I'd replace the nav lights with tested and certified LED nav lights. The issue here is 99% caused by bootleg replacement LED bulbs with crappy, noisy electronics in them. It's very unlikely there will be an issue using a certified nav light from hella, aquasignal, etc.