The results: zip-top bag and vodka lead the pack
The ginger stored in lime juice failed after just a few weeks when the liquid became cloudy and appeared rancid. All the peeled submerged ginger retained a definite ginger flavor (the sherry ginger came in last) and were still going strong at eight weeks, but the clear winner was the ginger stored in vodka, which produced firm, crisp ginger that still had a strong flavor.
The ginger stored in the vegetable crisper produced very diverse results. In this category, the runaway winner was the unpeeled ginger stored in a ziptop bag without any wrapping—the ginger stayed fresh, firm, and wrinkle-free for the entire eight weeks. The plain paper bag gave us wrinkly ginger after just a few weeks. The ginger wrapped in plastic and then put in a paper bag stayed fresher a little longer, but it still got wrinkly before the test was up. The paper towel wrapped ginger got moldy after a few weeks.
As for the ginger planted in soil, it stayed quite fresh, and it also yielded some lovely foliage, which may have been due to the fact that I feed my plants regularly.
In light of my experiments, I've decided to store my fresh, unpeeled ginger in a zip-top bag in my vegetable crisper, as long as I plan to use it within two months. Any longer than that, I'll peel the ginger and use the vodka method. I haven't tried this yet myself, but I'm guessing that ginger-infused vodka might make a great martini.