I think you concept is sound, I've seen others do exactly this.
Although, some of the problems that I've seen some others (Myself) run into are.
1) Depending on the micron size of the particulate filter, you may want a filter material that will filter somewhere in between your intake sponge and you micron filter used to polish the water. That way you have a filter for the large (Sponge on intake) particles, a filter for medium (I recommend gutting an old whole house filter and wrapping it with the blue cut to fit filter media for you application) particles, and lastly a filter for small (I use a 30 micron whole house filter) particles. If the last particle filter clogs much quickly than it should, then build another just like it and run them in parallel. This will also lower the resistance of the last particle filter helping flow.
2) I would consider another chamber dedicated for nothing but bio-media after the carbon.
3) Pump size is tricky when working with DIY filters. Hard (Not impossible) to calculate the filter resistance. I'd recommend a valve before the pump and after the last chamber to help control the water flow. As well as help in maintenance.
Just my 2 cents...