When the filter is changed, are you using the filter pads as biological filters (home for beneficial bacteria) or as chemical filters (for a week or so the activated carbon removes ammonia)? Of course we may use them both ways and, if the edge of the bag/ insert is stopping "big pieces" it is even a mechanical filter.

I wonder if a brand new dose of activated carbon pulls so much ammonia that the beneficial bacteria starve. Then in a week, when the activated carbon is "used up", there is more ammonia in the tank. Probably that is not the issue here though.

You are just rinsing the filter cartridge and returning it gray to the tank? That gets rid of the "big pieces." That way, all of the beneficial bacteria in there isn't washed away. White filter media means that it is sort of sterile or without any beneficial bacteria. Then you are restarting a part of the cycling process.

What you are doing is great but rinse the filter, not blast it spotless one week. The next week or interval, gravel vacuum 1/2 of the tank. The third week, do the other half of the gravel.

The water changes, if the water is previously treated and sits open a while, are wonderful. (Water treated in the tank may already be wiping out beneficial bacteria.)

If we see the whole aquarium as one big bio-filter (or biological system), that way the majority of the beneficial bacteria in the gravel and filter are not taken away all at once. And if there is enough beneficial bacteria in the gravel and filter then maybe the cloud, a bacterial bloom, will not form in the water.

I know that cloudy water is unattractive and I too would work to prevent it. However if the rest of the tank has been so thoroughly cleaned, maybe you are lucky that so much is being done in the water. :)