Forget the ice trick. It doesn't work. Put some cubes in a 5 gallon bucket 1/2 full of water and tip the bucket side to side. The cubes will move so slowly they couldn't possibly break anything up.
There are many different flushing wands available. I have one of the flexible Camco wands which I use only on occasion. You aren't going to thoroughly clean the tank in a minute or two either.
Water is your best friend in these situations. Fill, dump, fill, dump and repeat until you get the desired result. Not 1/2 or 3/4 full but FULL each time.
Chemicals can be helpful but only if you give them adequate time to work. Forget the recommended amounts. Sock the chemicals to it if you decide to use them. "Rid-X" made for residential septic systems is as good as any branded RV chemical and maybe even better. It is just a lot cheaper because it doesn't say RV on it anywhere. This is available nearly anywhere.
Driving around might accelerate the cleaning process but you could drive a lot of miles before you had any real cleaning action.
Id rather spend a few hours really cleaning the tank and getting it clean than driving around just to find the tank was still stuck up with s***. (Stuff)
2002 Fleetwood Storm 30H on Workhorse P32 chassis 8.1 gas.