With zero visibility, a streamer will serve no purpose.
Finding yourself several yards away from your target area sounds like current. This issue is easily solved with timing the dive. Slack tide lasts for aproximately 30 minutes. The depth of the soft, partially suspended "muck" at the bottom, along with water depth, will dictate whether or not the slack before high tide will be any more workable than the slack before the low. To be on the safe side, I would start with the slack before high. The deeper water will allow less turbulence at depth from surface movement of the water. During the slack tide, particularly prior to high tide, you may be fortunate enough to find a few inches or more visibility. Your chances of this will be greater if you wait at least 5 minutes into the slack before slowly entering your target area from the surface with smooth and minimal movement.
Dropping an anchor, along with your movement while hanging on its line will only cause more stirring of the "muck". Slim chance... but you might even crush the glasses with an anchor.
If your going to be sweeping your hands through the muck, though, visibility isn't an issue. A strong magnet, methodically swept through the muck may work... but only if there's any iron in the frame of the glasses.
Good luck and safe diving, my Friend!!!