I've been looking at this issue and at least your particles are not algae or bacterial bloom.
I liked the mechanical filter adaptation, but, as has already been pointed out, when you remove an internal filter, where the sponge is on the outside, 9 times out of 10, a whole load of gunk contaminates the water when you remove it.
This is precisely why I've learned to prefer internal filters where all of the filter media is inside the box...absolutely less mess when you want to clean the media.
You're touching on a good point here...
Think about the flow of water around the tank.
On the one hand, you don't want your fish battered and will need to create areas of less and more flow for them.
On the other hand, you want a clear path for debris to reach the filter.
A compromise has to be reached, but just a review of your internal tank layout might give you some clue towards improving the flow of contaminated water to the filter.