Until about 10 years ago, etrogim were wrapped in hemp (flax weed). It was messy, but it kept the etrogim fresh for much longer than the foam does. I also find that the combination of the foam and the etrog box (esp. silver ones) create more moisture, and eventually, mold.

Is there some place (in NYC area) where I can get etrogim wrapped in hay or just the hay itself? (I can do the wrapping.)

FYI - Most years, when I wrapped it in the hay and kept it in the cardboard box, it shrank minimally and did not dry out to the point where I was able to use it the following year. My current year's etrog is still fine and yellow and fresh-looking. If I can find some hay, now, I may be able to salvage it for this coming Succot.