DD has always trusted Snape, and he knew that he would have to beg Snape to get him to kill him. I think DD trusted Snape so much that he would trust him to take his life. DD knew he had to die in order for Harry to finally take on Voldemort (sort of Obi Wan-insh). I think he also didn't want Draco to do it because he knew that if Draco killed him, there would be no way for Draco to ever come back and turn away from Voldemort.
I think you nailed it. I just can't believe that Dumbledore would plead for his own life. Your interpretation meshes much better with his character.
I am starting to wonder about the potion (poison) DD drank in the cave. He said "it wasn't a health drink" and it obviously weakened him badly.
What if DD realized that there was no antidote for the potion and, realizing he was going to die anyhow, mangaged to arrange things so that his death would have the greatest benefit for the good side?