Interesting post starting up some nice conversations. I have a degree in the physiology of ageing and as far as I can see this new you in 7 years is a myth. As you said parts of you will have been renewed in full but others stick with you for your whole lifetime.
Even more interesting is that although cells are 'renewed' they are not actually completely 'new'. New cells need to come from somewhere and most of the time this is by the division of old cells involving the DNA of the original cell being copied. As you get older this division keeps happening but the 'ends' of the new DNA copy get shorter and more worn down with each division. The more worn down the DNA gets the more likely errors occur in the cell process e.g cancer/ the cell dying. Its this slow but inevitable wearing out of DNA that leads to old age and death.
There's tonnes of research ongoing about stopping these DNA ends (telomeres) getting worn away or regenerating them to combat ageing. And don't even get me started on the use of stem cells!