The shaded area sure sounds more like a sponge. I have a clear stringy sponge growing on the backside of my rocks where there is little light. Doesn't really spek to why its showing up in a brightly lit frag tank though. Reason I asked about eggcrate is because I have read a few threads in the past about a "snot" algae growing on it specifically. I reacll that having more of a reddish/brown tinge to it though.
Edit: Just did a quick search since I couldn't recall and it seems that those that gave the white eggcrate a good soak in vinegar and water didn't have any further issues and then there are those that went straight to the black, food grade eggcrate to avoid it all together. Not saying this is 100% your issue but worth looking into. Are you certain what you are seeing in your frag tank is the same as what is in your DT?