As a kid I had terrible Armegeddon nightmares about my non JW Dad being killed by God for not being a Witness or myself having to sacrifice my little sisters to the bad guys instead of giving into their torture to save them or myself. Looking back I realize that in between meetings my anxiety calmed somewhat only to be refueled again at the next one. As a middle aged adult the resulting lifelong difficulty I suffered with anxiety became almost unbearable at the end of my JW career. Meetings and any kind of talk about the last days would trigger heart palpitations and stomach flip flops which could only be alleviated by stealing out to my car where I began stashing a small container of beer or wine to quell the symptoms. This was a drastic move for me as a virtual non drinker, and a clue that something had to be done. Upon my subsequent self directed exit from the Org. My anxiety disappeared overnight and has not returned in almost 5 years. It has been such a relief and well worth the loss of every friend I ever knew.
If you can convince your family that for the sake of your son you need to take a little break from anything having to do with death and destruction or talk of the end of the world until he comes to grips with the obvious trauma he has suffered from exposure to all this dooms day talk, it might be the queue you need to make a long term exit. It is completely understandable how a ny kid who is truly listening at the meetings could be frightened by what he is hearing over and over from the adults in his little world.