Is there a particular diet that has been quantitatively proven to increase lifespan and overall healthiness (blood pressure, etc) of individuals?

I do not know the: Level of detail you expect, but the mediterranean diet has a bit of data to support its positive effects. Also, dr. Dean ornish has a diet that appears to be able to reverse heart disease, but it is very strict. Try web searches of them.

Mediterranean: A mediterranean diet has been associated with longer life span. There are no randomized controlled trials that "prove" this. The dash diet has been shown to lower you blood pressure. With a lower blood pressure you will lower your risk of heart attack, stroke, and kidney failure, and thus live longer.