I had the same problem this summer. The tanks were full and would not drain. I put in a bottle of Rid Ex. I then let it sit for about 4 hours. Finally I took a snake and ran into the hose hookup side and worked it pretty hard until it started flowing well. I then took a water hose and ran it inside and flushed out all kinds of debris.
For storage I put in more Riddex and some water and also some Antifreeze.
I was told that you never want to leave the tank dry, when storing.
As for adding Ice, probably in your case not going to work if the tank is full. The clog will be at the bottom of the tank. And the ice will be floating at the top. Good luck.