http://www.theplantedtank.co.uk/algae.htm
http://www.csd.net/~cgadd/aqua/art_plant_algae.htm
http://www.plantgeek.net/article_viewer.php?id=9
http://www.plantedtank.net/articles/Algae-Common-Types/3/
http://www.guitarfish.org/algae
1) raise that light back up
2) add a floating plant
3) try excel or h2o2 if you'd like... an h2o2 dip outside the tank would be faster, easier and less risky.
4) check your nutrient levels... there's a list in the guitarfish link of where they should be
5) definitely check your ammonia
java moss falls prey to algae easily, especially if there's too much light.
you could consider an air stone for a little bump in co2. there is more in the atmosphere than in your water so it could help.
buying more moss is not necessary. you'll have the same plant that's incapable of doing it's job in the same setup you have now. then the new moss will have to acclimate to it's new environment. if you miss any algae or what the cause is you'll be back to square one with a plant that's not properly acclimated. it could make it worse. you could introduce something new to your tank to deal with also.
a floating plant will have the added benefit of being able to take co2 from the atmosphere where it is abundant and providing shade for your moss.
amano shrimp could help... just maybe.
if you do still decide to change out your moss take it out slowly. don't shake it anywhere, especially your tank. once it's in the bucket spread it out thin and let the shrimp have their space. once it's spread nicely they should just swim out as you slowly lift it.
good luck, that looks like a nasty mess in a cramped apartment.