It sounds like you're using old rock, and 3 yr old sand, which was disturbed during the tank move. Either, or both could be leaching back into your tank. Some you can test for, and some you cannot. IMO, you should stay on top of the water changes, and physically remove all of the algae that you can until things stabilize. I personally, do not believe that it's a source water problem. My tanks both run on on tap water with no skimmer. (Not the preferred method, but to each his/her own. Your mileage may vary.) The last time I tested, my TDS at the tap was close to 800. I suspect that your probs are related to the the rock/sand from the old system....not your choice of salt.
My .02