"This means that you essentially have a new body every 7 years."
But ... but the information to build my proteins and not yours is still stored in my genes! :)
If my DNA is copied atoms and molecules can get replaced/added but the general structure of the DNA and thus the genetical information to construct my body stays more or less the same for quite a while (I am aware of mutations and the process of aging ...).
Imagine you replace a wall in a house. When you rebuild it you use the same architect's drawing ... that leads to the result that the house will be "the same" again like before even if the stones are not the same anymore.
The idea of that house is still the same!
Thus I add a possible answer to yours: "I am myself because of my genes which contain the information to rebuild all my proteins again and again in the same way (even if using new atoms an molecules)!"
Yeah, that's a very good answer. Genes, or rather the information on genes might be the answer to the question. Only one thing that could be argued against it is the cloning process I mentioned above. But I think that might be the closest it gets! Good job :)