This problem has been resolved. I found out what the problem was and corrected it.
Dragging? That's not what you do...(so what if it took forever for me to figure it all out...)
You need to click on 'Tools' in SM, then find Import Custom Sprite and click that. Select the sprite you want and click it and it gets added at the end of the section list. Weapons have a 'custom sprite' thing under the ED2 part of the GUI.
...and what do you mean by 'columns'? O_o
Actually, there's an easier way. Click 'Tools' and go to 'Group Arrange'. There you can see four "groups" of sections, and can delete the ones you don't want. Then you can mass-select a bunch of sections in a folder and click-and-drag them into one of those groups. After that, you press Esc to leave Group Arrange mode and can Save the Custom Sprites Ini so you don't need to load them all into SM again. Easy as breathin'.