Thanks for the info Greg!
Well that eliminates the hot water tank possibility since you used cold water to fill the tank. Yes you can use a combination of hot and cold water for future tanks set ups and water changes, much easier than needing to bring the cold water up to temperature before using it.
I doubt your filter media needs to be rinsed again especially on such a new tank. However, you may be able to add some polishing media such as filter wool/floss or Poly-fil Traditional Batting (found at fabric store) to help catch small particles. These type products are placed in the filter according to the filter instructions as the last media prior to the water exiting the filter.
Can you post the brand and model of your filter, I couldn't tell from your 1st posts which one you have? Also, what media are you using in the filter AND do you have the Purigen in it's media bag?
It can be difficult for a filter to pick up these type of particles as they tend to disperse throughout the water column especially if 'something' is still causing the particles to appear. Texas Holey Rock, if not thoroughly rinsed well could still be shedding particles but I'm not sure.
Could you post your water test results for ammonia, nitrite, nitrate, pH and if you have them, GH (hardness) and KH (alkalinity)? Also post the brand and type test kit you are using.
To answer your other question, a diatom filter is a specialty filter that uses diatomaceous earth to remove tiny particles and trap them as well as polish the water. They should still be available for aquarium use but can be a pricey item for the occasional use. Maybe ask your local aquarium specialist if they have one that you can borrow, just be sure it has been cleaned and recharged with fresh DE so as to avoid transferring any illness to your tank. Some people also make a DIY bottle filter filled with filter floss or similar material and use an air pump or powerhead to remove small particles from the tank.