This article about Method 1 and Method 2 gives a brief explanation of Methods 1 and 2 in terms of dispatching flights under 14 CFR 121. Here's an excerpt.
FAR 121.191 requires that we dispatch our aircraft on a routing, weight and expected enroute temperature, that complies with a minimum terrain clearance requirement after an engine failure.
It also requires that we have a plan in place that allows a diversion to an alternate airport enroute, following an engine failure and drift down, with a specific terrain clearance if we do not have the performance to continue to the destination.
My question about flights dispatched under Method 2 concerns route changes. In practice, I'm quite sure that pilots operating aircraft with a Method 2 dispatch release deviate from the planned route on the dispatch all the time. Reasons might include a shortcut request to air traffic control or deviations for weather. Weather deviations seem like the most relevant here because they can sometimes be quite significant.
What additional considerations do pilots have when accepting route changes on flights dispatched under Method 2? Couldn't changing the route render the Method 2 calculations irrelevant?