I don’t think Dumbledore would have made a Horcrux. Splitting ones soul apart was spoken of very negatively, and I couldn’t see Dumbledore doing it. He certainly doesn’t seem to have that not-quite-living thing Voldemort has.
Did anyone else love the start with Tony Blair? Ok, sure, it only said “Prime Minister,” but I was definitely picturing Tony Blair.
And finally, this theory could be way-off - there are many things wrong with it, but is it possible Harry could be one of Voldemort’s horcruxes? Perhaps the bit of Voldemort in him is a horcrux, perhaps created when V killed Lily? Which would mean the only way to get rid of Voldemort fully is for Harry to sacrifice himself.
Just an idea.