So, turns out you can grind ginger in the garlic press, but there's one significant catch. It works at a much higher pressure, meaning (a) you need a strong press, (b) a strong hand, and (c) the ginger flies out at such high velocity (and from both sides, somehow) that it's pretty hard to contain. In other words, the kitchen is a complete mess now, but I didn't break the press 👍