Jason's the expert here, and his advice parallels what I've seen elsewhere...
However, since you also said you're fighting a massive algae problem, it might be something different too, so I'll chime in with my 2 cents (I dealt with the same challenge recently)....I saw a site a few weeks ago (when I was dealing with the same issue) that had a different explanation than the normal "metals in the water" answer...I can't find the link now (of course!), but they showed pictures of a pool with brand new fill water that had a residual green tint like you describe, and they attributed the tint to the existence of tap water chloramines (and tri-chloramines, in particular, IIRC). They said they see it a lot when filling new pools, since many municipalities apparently have high chloramine content in their tap water, and the chloramines apparently have a naturally light green tint to them?!? They said shocking away the CC would remedy the problem...and they talked about this in terms of the pool's initial chlorine demand on startup (if that helps with your Google searching!).
Their explanation (coupled with pictures that looked eerily similar to what I was seeing) seemed logical to me, and since it sort of mirrored my algae situation (I didn't have new fill water, but I'd definitely been shocking the heck out of the pool, but was still struggling to really stay ahead of the curve and get rid of my CCs), and because I didn't have any reason to suspect metals when I'd never had any before, I tried their approach and had great success.
Jason's suggestion is to wait for FCs to drop and see if the green goes away, which might happen either because 1) your FC/Metal interactions drop below visible levels of greenness, or 2) it might be because your CCs have gradually oxidized away and lost their natural tinting impact on the water...The only downside to this approach of Jason's is that if your water is green either b/c you 1) still have some algae, or 2) because your CC's are really high...In the first case, waiting could either let the algae come back, and in the second, you might be waiting a long time to get to a point where the CC's oxidize within a reasonable time...So I'd bias towards continuing to shock, lest all your previous shocking and brushing work be in vain...The downside to that approach is that it obviously costs money for the shock, and, if you do have metals, it might make the problem worse!
Good luck!