I wouldn't ditch the basket.
I used a fluval 103 on my 20 gal community tank. Do you have 4 foam filter pads in the filter? They also hold bacteria. Where you have the plain beads for separating the debris out first I also stuck in a thin fiber pad too. There is lots of places for the bacteria to hide-- even up on the walls of the tubing, all over the gravel surfaces and on the glass side walls.
It will not hurt the bacteria to be out of the filter/water for a few minutes. When you wash the junk off the foam pads just rinse them in the old tank water-- never tapwater!!
Rinse the bio max beads off in old tank water too-- it will wash out some more junk as well as any bacteria that have died and gone to the great beyond.
Do not be too clean in the tank!! Ie if cleaning the gravel really well don't do the filter the same week and vice versa. I learned that the hard way and put my tank thru another cycle!
