One of the reasons
AC filters are so awesome is becuase of the ease at which you can move media around. if the other filters are cycled, then all you need to do is swap out the biomax from an established tank for the new stuff. the sponge will preserve the cycle in the old tank and the old biomax will instantly cycle the new tank. i would cut back on feeding the old tank for a few days to let the bacteria catch up. ive done this a dozen times without fail.
youll need to add fish as soon as you transfe3r the biomax to keep the cycle going - i dont think the shrimp will decompose fast enough to sustain the established colony.
in any case, if youve already got an established tank, you dont need to do a fishless cycle unless you want practice.