GFCI breaker tripping mysteriously
I recently installed some outdoor receptacles for stock tank de-icers for a horse farm. They are regular 120V receptacles, but since I have to power six 500-watt heaters at six different locations, I chose to run them on two different circuits. Otherwise I would have had to use really large (and really expensive) wire to put them all on one circuit. I ran a single 12/3 wire to all six receptacles and staggered the hot connection (so the first one used black, the second red, the third black, etc.). They all share a common neutral. Thus, three of them are on one pole, and the other three are on the other pole.
Obviously I want these outlets to be GFCI protected (not to mention that code demands it). With a shared neutral, of course, I can't just use two single-pole GFCI breakers. I either have to use separate GFCI receptacles at all six locations or use a two-pole 120/240 GFCI breaker in the panel (which is a Cutler-Hammer BR series, by the way). The cost is about the same in both cases, so I chose the second option.
I got everything installed, flipped the breaker on, verified that all the outlets work, made sure the "test" button on the breaker caused it to trip, and gave myself a pat on the back for a job well done. Then later in the day, I was in the barn where the electrical panel is located and I happened to turn on the fluorescent overhead lights. Just as I did, I thought I heard a breaker trip in the panel, but the lights were still on, so I figured I must have been hearing things. Nevertheless, the next time I walked by the panel, I checked and the 2-pole breaker for the tank de-icers was tripped! So I reset it and tried to duplicate the behavior. Sure enough, after a couple of tries I got it to trip again by turning the fluorescent lights on. That left me really scratching my head, because they're on completely different circuits. Clearly the lights couldn't have been causing current to flow in either hot leg or the neutral in the de-icer circuit!
Then later in the day, the breaker tripped again at some point when nobody had been in the barn to turn lights on or off (though there's a hot-water heater on a different circuit that cycles on and off). And to make matters even more confusing, there was ANOTHER breaker tripped. This time it was a GFCI/AFCI single-pole breaker for some receptacles in the barn. The only thing plugged into those outlets was a 200W heat tape that keeps some pipes from freezing.
So now I'm really confused! At first I thought maybe the two-pole GFCI breaker was just over-sensitive and needed to be exchanged for a replacement (even though I still can't figure out how flipping a switch on a completely different circuit could trip it). But with this second breaker now tripping, I can't make heads or tails of what could be causing this. The only possible explanation I can come up with is that there's an electric fence nearby the trench where the 12/3 wire runs. There are often times throughout the day where the fence contacts the ground, so I suppose it's possible that return current from fence is somehow coupling onto the 12/3 line underground and getting back to the panel and causing various wacky behavior. That really seems like grasping at straws though.
So does anybody have any experience with oversensitive GFCI breakers? And can one breaker tripping cause another to trip? Any other ideas as to what could be going on here?
Thanks for your help!