The gist of the issue is that ArcMap is rendering most of my NoData values as the minimum stretch value color instead of the NoData color. My dataset is for global production of soybeans, so most of the world should be NoData (where there is no soy grown) and then some value between 0 and 27000 where there is soy grown. If I do a stretched symbology and set NoData to no color and use a gradient for the values (say black to white), all of the NoData values on the earth are rendered as black. I'm working with the Robinson projection, so my globe is kind of an oval and the corners of the map are empty. These empty corners, which also have NoData values, render correctly, but on the globe itself, they render as the lowest color available. If I do classified colors, all the NoData on the earth renders as the lowest class.
If I zoom in so that the whole data frame is the earth (get the empty corners that render properly off the screen), then my NoData values start working. It's almost like there are 2 types of NoData that are fighting each other and it's only when one is totally off screen that the other behaves.