I would like others to give their input here to be certain but I kind of doubt that the drain snake would add enough iron in the water to result in staining levels of iron being present in the water. Rather, I would look to the fill water to be a more likely source. Are you filling from a well? If so, and the well water is high in iron, you may continue to run into the same problems. A metal sequestrant might be the way to go in that case. Sounds like your proximity to the marsh would make draining your pool a touchy thing at best. I'll defer to the experts here for the best advice.

I would get your fill water tested for iron before doing any water replacement. Fill water is by far the most likely source of iron in the pool. If your fill water doesn't have any iron, then water replacement is a good idea. If you do end up doing some water replacement, you will need to be careful not to let the water level get very far below where it is now.