While keeping berries fresh is something we'd all like, keeping as many berries fresh as possible is even MORE important when you don't have a lot of food choices and those berries are essentially your sweet bastion against the boring food world.
So, check out this article: http://www.nytimes.com/2009/08/26/dining/26curi.html?_r=0
Essentially, what it says is this:
To keep the mold from developing, try a very quick heat bath.
Strawberries, raspberries, and blackberries: 30 seconds at 125 degrees (water bath) would do it.
Blueberries (with thicker skins): 30 seconds at 140 degrees (water bath).
The article's author simply immersed and swished the berries in the hot water bath without removing them from the plastic basket - just dunked the whole thing.
Sounds like something to try out!