That's an interesting point. I'd even go a step further and say that which of those two definitions is true determines whether time travel is possible. Put another way, conservation across space-time (instead of a single point in time) is necessary for time travel to exist, and the existence of time travel is the only reason conservation would be across space-time.
I'm not sure that time travel is the only reason - it might turn out to explain some other peculiarities in the universe (spooky action at a distance jumps into my mind as something that could potentially have an explanation linked to this).
It also would seem to be impossible to calculate energy at a specific moment. Energy = mc^2, or expressed differently, e = m * d^2 * t^-2. If t = 0, then t^-2 is not calculable.
If instead the rule is that we need to conserve the energy sum of all possible locations in space-time, then no law is broken.