Don't give up just yet. To me it looks like a type of cyanobacteria, due to a chronic nitrate shortage. I had it briefly when I got lazy one week of not dosing. You need to dose Nitrogen, siphon out as much of that stuff possible. I'm sure at your stage over-dosing nitrogen might not work. I would get a UV sterilizer. And run that for a couple weeks. Hope that helps.
Grey slime does not appear to be an alga at all, but rather a cyanobacteria similar to the 'BGA' we all know and love. It varies in color from greenish to a dark grey.
Grey slime may appear as upward growing strands, as a coating on the edge of a leaf, and as what looks like floating mucus. It can pearl heavily and with its rapid growth, can totally smother a plant. When disturbed, this cyanobacteria disolves into a greyish haze in the water.
How to Treat: Grey slime is induced by chronic nitrate shortage, and one will often notice the presence of BGA preceding its appearance. Adding pressurized co2, replacing old light bulbs, and letting the total plant mass in the tank get out of control are all things that can make nitrate levels crash if care is not taken when these kinds of things are done. It is relatively difficult to combat once present, as raising nitrates to proper levels rarely works.
Prevention is the best medicine, so a good nitrate test kit and adequate fertilization go a long way.
If it does show up, there are not many ways to get rid of grey slime. The most effective method is to do a blackout lasting about four days. Doing that in conjunction with a diatom filter and several large water changes definitely helps.
An ultraviolet sterilizer may work, but it may have negative effects on trace elements in the water column. For that reason, it should only be left on temporarily.
A final option that does not work as often is to totally rescape and clean out the tank. It's somewhat of a mystery as to why that works, but it may be that it shocks the slime in some way.
Dosing the tank with erythromycin does not appear to be effective.