Live rock is only one kind of filtration and there are so many other options you can go with instead.
For filtration, you mainly need to address dissolved organics that make the water go yellow, phosphates and nitrates.
You could use a Marine Pure plate as a substitute for live rock biofiltration, seed this with Dr Tim's One & Only Nitrifying Bacteria when you cycle the tank. The plate can be buried in the substrate to hide it from view.
Depending on how much space you have in that HOB filter you could try a combo of some of the following, I'm sure there are even more options than what I'm listing:
Purigen
Poly-Filter
Chemipure Elite
Phosphate RX
Biopellet Reactor
Microbial cleaning products
Activated Carbon
In-tank skimmer such as a Tunze Comline model or Auqa Ghost
There are also some options using an automatic doser such as carbon dosing and the Zeovit system