Storing Biological Media and Rock

I would just rinse everything out really well, and let it completely air dry. Then bag it in ziplock or something similar. Depending on how old the sponges are, you might just replace them. The gravel will be fine to reuse too. Just do the same as above and make sure it is clean and dry so it doesn't get moldy

How long of drive? You probably can keep it alive if you put it in some tank water and in a cooler to keep the temp stable.

i would just get a tupperware container or styrofoam cooler, rinse everything in tank water to get rid of most gunk, and put rock and water into it. keep it in the car with you and take it into your hotel room at night, the temps should be fine. the back of a moving van is just too hot. that way you can set everything up easier without having to cycle your tank again. depending on how long you're without fish you may want to keep your test kits handy and feed your bacteria with ammonia to keep it alive before the fish come.

mostly it just depends on whether you want to cycle again in your new home.

I would just try too keep it alive by placing it in a bag with tank water, adding drops of ammonia everyday. This way you don't have to cycle when you get there.

just take enough to cover the rock and keep it wet. it's not the water that helps the cycle, it's the bacteria living on the rock and gravel. very few of them are free-floating. the only reason we suggest tank water is because, well, it's right there and already treated to be safe.

i would add a couple drops daily.
make sure it is pure ammonia. one way to tell (other than reading the label) is to shake it, if it gets foamy on top it is not pure.

I don't think you will need to be carrying an eyedropper and ammonia with you (what a PITA). And you don't need to "rinse the gunk off either. (that gunk is decomposing food that is creating it's own ammonia).

Get some of the big bags from you lfs and bag everything as if it was fish (just enough water to cover rocks). Ask an employee to show you how to get that nice "puffed up" look to the bags. Place this in a big cooler and add a couple of 44oz cups of ice from a convienient gas station to the cooler once a day. At the same time as you add the ice, open the bags to let in fresh air and then close them up again. If you don't open the cooler this should keep the temp cool, but not cold. This will slow the bacteria's metabolism so that they really won't need any extra feeding. If you feel you must, add a pinch of fishfood when you are opening the bags.

Our bacterial friends may be slow to reproduce, but they are tough little suckers. A few days without food is not even going to make a dent in thier population. Case in point: "Live Rock" sold for marine tanks is shipped in wet newspaper for several days before it gets to the lfs. The bacteria come through just fine.