Filter clogging

I have about a 300 gallon plastic pond with a submersible pump that
has a built-in "cage" that holds a fist-sized filter. The water is
pumped up to an external biological filter and also to a waterfall.

This spring the pond was so pea soupy that I totally emptied it and
started from scratch and added a net bag of Barley pellets.

In the pond, I now have water hyacinths and lettuce and also an
oxygenator growing well, along with about 6 goldfish. The water is
clear and there isn't much sludge, if any on the bottom of the pond.

My filter is another story. I am finding that I have to hose it down
EVERY day. It is clogging up with sludge and tiny plant bits so much
so that my waterfall completely stops.

If I keep the cage part of the pump attached, do I HAVE to have the
foam filter in there? The cage has 3 to 4" long slots along the side.
A fish could not get in there. Will the pump be able to run without
clogging up, too?