I'm a little confused as to your set up really.
It sounds like you have some 12v car or marine batteries and don't mind using their juice on your tank? From looking up the Fluval Aquaclear 70 it only has a power draw of 6w. You could run this off a typical car battery for something like a week if you wanted to, at least a few days. You would just need a 110v to 12v step down transformer - which I guess is too late to get now.
What are the sponge filters you are referring to? I guess you are going to drive water through them using these 12v aerators?
By the way, don't get too worried about bio rings, bio balls etc - they aren't needed. They are meant to increase the surface area and therefore increase the bacterial colony size and therefore the amount of bio load the filter can handle. Which they might well do, however the bacteria don't care, they will colonise everything in your filter, including all the sponges.
This whole mechanical stage, bio stage and chemical stage (ie carbon) in filters is a bit of a nonsense. The whole filter is your biological filter. My external filter is currently different layers of sponge, with some ceramic stuff I brought from the previous filter to "seed" this one.
And yes, if you filter is slimy, then clean it!
I won't feed the fish anymore! No matter how much they beg. The little shits.
That's the spirit!
Good luck!