Not really a way to clear it up faster.
Monitor the ammonia. As protein decomposes it raises the ammonia level. I have often seen cloudy water when the ammonia level if rising.
Do enough water changes (frequency and volume) to keep the ammonia under .25ppm.
To do more water changes with less stress to the livestock you can do this:
Make a batch of new water that matches the old water (GH, KH, TDS, temperature). Make enough to fill the tank at least once. (so if you have a 20 gallon tank, make 20+ gallons of water)
Start a siphon in the tank, and start a pump in the container of new water, pumping the water into the tank. Clamp the tubing to the tank in a way that sheets the new water across the surface.
You can use the siphon to vacuum near the bottom of the tank to pick up more debris that can also contribute to ammonia, or cloudy water. Just stay away from where the new water is entering the tank.
Keep the siphon and the pump synchronized so the water level goes down very slowly.
Since you are adding new water at the same time as removing it there is some blending of the water, so you are removing some of the new water with the old.
The net result of a water change like this is roughly the same as 50%.
ie: If you use 20 gallons of new water during this, and you have a 20 gallon tank, it is like doing a 10 gallon water change.