For those following this thread, I bought the inTank "Chamber One Media Basket for Waterbox Cube..." Unfortunately, it didn't work. It's really hard to get it captured in a photo, but in the overflow chamber, just below the holes, there's a protrusion that starts on the corner adjacent to the side wall that juts out. The media basket wouldn't fit, and because of the issue being a 2 mm or so protrusion running down the whole side down from the holes, I would have to try to saw a chunk out of the whole thing. I gave up on the media basket, but I was still really tired of the sponge. I decided to try the filter floss holder from InTank as an alternative to the media basket. I had to cut a little chunk out to address the protrusion I mentioned above, but it was doable (see pic below). I then added ChemiPure Blue into the overflow chamber (see pic). My water has cleared up so much since I did this, especially at the top. I also added a Tunze Turbelle Nanostream 6015 and that has helped with flow.
Because I'm using ChemiPure Blue now I removed the two Aquatop Media baskets that had phosphate reducing media and carbon media, and added a box of MarinePure balls on top of the two baskets holding the Aquatop bio-media.
Overall I am happy with my mods and recommend them. I am in the apparently distinct minority of Aquatop aquarium owners who are satisfied with the included skimmer. Mine has been great about pulling brown stuff out of the water.