Wow, great advice here.
It sounds like a tough situation for you because the dog is fearful, but also now might be conditioned to getting "good" results (not being left alone) from negative actions like whining.
I have an assistance dog trained by Dogs for the Deaf, and because of the strong bonding created with the human partner, was taught by her trainers to also be sure I left her home alone from time to time to lessen the chance of such anxiety developing. I sprinkle some yummy treats (there are anti-allergenic versions) on her bed and leave a TV on. Now I think she looks forward to it.
I think the Kong advice was definitely worth trying. Our trainer suggested using yoghurt, treats, dabs of peanut butter at one end, and various healthy foods the dog likes. The Kong website probably has lots of suggestions. Stuff the Kongs and freeze.