There's a lot of misinformation in this thread.
A proper reforging tool utilizes one and only one method—it calculates every possible combination of reforges, multiplies the resulting stat totals by the given weights, and picks whichever combination yields the highest total value. The reason that sites like AMR often suggest reforging slightly under the hit cap is because that particular combination yielded the highest result. That's it. And for the all the love that WoWReforge seems to be getting, WoWReforge does not utilize this method.
Now, whether or not the stat weights that you're inputting accurately reflect the change in DPS that you'll see from increasing or decreasing those stats is another matter entirely. Tools like SimCraft or ShadowCraft can probably give you a better set of weights to use than whatever AMR is suggesting by default. But rest assured, AMR will tell you how to optimally reforge your gear for any given weights.