Does Reach Spell only add to the original casting, or also during the 10 minute duration?
That is an interesting question. I was inclined to say that it adds to the 10 minute duration, but at the same time, within the spell it declares that if the target is ever more than 30 feet away from you, the spell ends. I would say that if the text of the spell had said something to the effect of, "If the target is ever out of the Range of the spell..." then it would count Reach Spell.
As written, I'd rule it ending if the target was outside of 30 feet of you at any time, even though the range of the spell would be increased by Reach Spell.
We did play it as such--only 30'--and it was difficult keeping within 30' range!
I think it applies the entire time, otherwise it would do nothing, as the spell would fail the instant you cast it. It's clear that the spell says 30 feet because that is the Range. Reach Spell would simply change all instances of 30 feet to 60 feet.