AI traffic shows up with no problems at KJFK, the only thing that might stop displaying it, is using FS9 models in FSX (not really suggested, for performance reasons too) hand having the "Aircraft case shadows on ground" on. Using an AI Traffic pack that has native FSX models, like UT2, doesn't require to turn off the aircraft shadows.
But, you said you already tried it. Another possible explanation, your Traffic.bgl is in the FS9 format, which is also not good in FSX.
Basically, I think it all boils to using something ported over from FS9 (World or AI, for example) and not native.
Another thing to check are AFCAD conflicts created by a duplicate AFCAD from another product, use the free FSX Airport Scanner to find AFCAD duplicates and remove all the extra, except the default one from MS and the one in the fsdreamteam\JFK folder