Tried a batch chopped with a knife. Much weaker than the stuff run through the food processor. Wife gave it a thumbs down.
Next batch we subbed 1 cup brown sugar for one of the four cups of sugar and ran a pound of ginger through the food processor, but cut the water down to seven cups, brought to a boil and simmered for forty minutes.
Best batch yet. This is going to be the default from now on:
One pound unpeeled washed ginger, cut into chunks and processed for about five one second pulses
Three cups sugar
One cup brown sugar
Seven cups water
About 1/2 tsp kosher salt
Bring to a boil, simmer forty minutes, then run through a mesh strainer a couple times while still hot. I press on the solids the first time it's strained to extract as much gingery liquid as I can. If a clear syrup is desired, I'd run it through a cheesecloth once, but the wife and I don't mind the sediment that the mesh strainer allows.
I use about two to three tablespoons (I eyeball it) in a zombie glass of club soda or seltzer water, and a splash of lime juice.