Interpretations Unstuck in Time

For those that have known me or have read my writings you know that I am a fan of the great Kurt Vonnegut Jr.  That being said, his wonderful opus magnum "Slaughterhouse-Five" is one of the most influential and meaningful writings to me.  I have read the book many times a long with many writings about the book and Mr. Vonnegut in general.  None of these writings have ever answered one question within the book that has always bothered me and I hope that some of my readers might have an opinion on this.

In the book, our hero Billy Pilgrim becomes "unstuck in time" and slips between various times in his life.  His life leads him down a path where he becomes abducted by aliens and taught to see life like a mountain range, each peak being another point in time.  This leads Billy to hit any moment in his life and know exactly how it is going to happen, even up to the exact moment of his murder as well as how and who cause it.  This being said, Mr. Vonnegut weaves a brilliant story with simple and understated references to colors and actions that help flip Billy between memories.  These things help us to believe that Billy's "unstuck-ness" is really just his mind slipping around between memories and times due to either some mental issues or PTSD from World War II.  He is really crazy and battling to keep his wits in a world full of hate and death that he cannot handle.  He invents the aliens and their world as an escape route, finding that the only reason no one stops the violence is because they can't, it has already been written into 4-dimensional time, and therefore, it is, no matter what anyone does.

As brilliant and wonderful as this interpretation of the book is, as well as being the prevailing viewpoint, there is at least one huge question that bothers me about this.  We take the narrator's description of what is going on to either be literal or metaphorical.  Either the events are true and Billy was taught by aliens, or Billy is suffering from trauma.  I do not believe there is much room for a grey area here.

If that is so, if Billy is crazy as the books aims towards, then how is it that Billy knows, 100%, the moment and style of his death?

Billy tells everyone how he is going to die, and when.  It happens exactly as he knew, as if he knew the exact future.  The only way that I can reconcile this is that Billy was not actually murdered as he said, but even his own death is a created memory from his trauma.  This does not sit well with me though as that implies he fantasizes about his own murder.  He then must want to die to prove to himself that his memories were real.  This just does not make sense to me because the book, at least in my reading, makes not reference to this as a created memory as it does with everything else.  The book appears to treat it as reality.  Also, if Billy wanted to fantasize about his death to prove his life, then there were other points where this can be made reality.

Please, if any of you have an opinion on this interpretation, let us discuss.  Comment or email me directly and we will go into discourse.  I even asked this question on some KV forums and no one seems to have a direct answer to this either.  Any ideas will be discussed.  Thanks!