... Cans almost as close but a bit further have almost no deleterious effects.
One of the interesting characteristics of digital TV is the ability to automatically correct a large number of small errors in the digital signal.
Typically there is no easy to see indication of just how hard the TV is computing to fix errors in the received signal, so the interference can increase progressively with no apparent ill effects until it crosses that threshold of possible error correction and starts to show problems in the picture.
As the interference gets progressively worse from there it can lead to seconds at a time of complete dropout of the signal (the image may freeze or it may just break up.)
It really sounds like your problem is radiated energy hitting the antenna, rather than conducted RF over the wires, so there is no much you can do to keep the RF out of the antenna wires. Possibly putting an RF filter right at the connection to each can will help, as may being sure that all the metal parts of the can and trim are bonded together (grounding alone probably will not help.) If part of the trim is plastic rather than metal, making an aluminum foil hat for it may actually help.
Try dropping the trim down while it is still operating and changing the orientation to see if it selectively radiates RF in one set of directions.
Based on other reported experiences, the best remedy possible will be to replace the LED/driver combination with a different brand, trying first a brand that has been reported here to be interference free. You can replace one can near the antenna first and test with it before going all the way to replace all of them.
