The marineland eclipse series corner crescent system there are a couple simple things you can do to the original filter system.
Add a fluval pre-filter sponge as used on fluval edge tanks.
Tilt the filter cartridge up so the bio-wheel end is higher.
Keep a jug of treated water near the tank to top off the water level every day.
My main beefs with the marinelands is the speed at which their cartridges clog... its terrible how effective they are at straining material out of the water, you can rarely get more than a week out of them! and their sensitivity to water level.
The water level is the only thing you'll need to worry about if you put the sponge on and tilt the cartridge.
Honestly with the sponge in you can get away with using tea-bags filled with bulk carbon up top.
One of the most common clogging situations on filters is as simple as over-feeding. In the end the bacteria get to eat everything, if you filter is clogging with brown then you're either overloaded, overfeeding or have messy fish (overloaded) that tear stuff up. The bio-wheel in the eclipse series is where the bacteria should live but if you're not using that you'll grow new on the tetra's bag every time. Pre-filter sponge is WIN again.