You are not doing the fishless cycle unless you are feeding the bacteria.
What you are doing is allowing the plants to root, or running a very long test on the equipment. But not growing bacteria.
Feed the bacteria ammonia.
Read the label on the bacterial additive you have used. Does it include nitrospira? If not it is the wrong species of bacteria, and could be some of the heterotrophic bacteria that are clouding the tank.
You can do water changes to remove the cloudy water, but if there is still food for the bacteria they will just grow back. Eventually their food supply is greatly reduced (they have eaten it all) so the population goes down. Nothing you really need to do about it. Just wait it out.
The other possibility is a problem with mineral levels. Pure RO water has no minerals. Any minerals from any source (decorative rock, substrate, pH altering products) can cloud the water.
Here is what I would do:
Test the GH and KH, bring them both up to a minimum of 3 German degrees of hardness, higher is better. Nitrifying bacteria need some minerals and carbonate. They will not live in pure RO water.
Test for ammonia, nitrite and nitrate.
Start feeding the tank ammonia. Make sure there is 3 ppm of ammonia.
Then test the next day, then the next. Same tests.
If the additive you used is the right bacteria, and they have not died (being in a tank with no food and no minerals) then you will see ammonia going down, nitrite and nitrate rising. By about the third day the nitrite will also drop and all you ought to see is nitrate.
If there is not a significant population of the right species of bacteria then the ammonia will remain at 3 ppm or drop very slowly, and little or no nitrite or nitrate will show up.
Option A) Go get the right species of bacteria (look for nitrospira)
Option B) Continue with the fishless cycle.
Option C) Combine A and B.
Here is the fishless cycle.
You too can boast that "No fish were harmed in the cycling of your new tank"
Cycling a tank means to grow the beneficial bacteria that will help to decompose the fish waste (especially ammonia). These bacteria need ammonia to grow. There are 3 sources of ammonia that work to do this. One is fish. Unfortunately, the process exposes the fish to ammonia, which burns their gills, and nitrite, which makes their blood unable to carry oxygen. This often kills the fish.
Another source is decomposing protein. You could cycle your tank by adding fish food or a dead fish or shellfish. You do not know how much beneficial bacteria you are growing, though.
The best source of ammonia is... Ammonia. In a bottle.
Using fish is a delicate balance of water changes to keep the toxins low (try not to hurt the fish) but keep feeding the bacteria. It can take 4 to 8 weeks to cycle a tank this way, and can cost the lives of several fish. When you are done you have grown a small bacteria population that still needs to be nurtured to increase its population. You cannot, at the end of a fish-in cycle, fully stock your tank.
The fishless/ammonia cycle takes as little as 3 weeks, and can be even faster, grows a BIG bacteria population, and does not harm fish in any way.
Both methods give you plenty of practice using your test kit.
How to cycle a tank the fishless way:
1) Make sure all equipment is working, fill with water that has all the stuff you will need for the fish you intend to keep. Dechlorinator, minerals for GH or KH adjustments, the proper salt mix, if you are creating a brackish or marine tank. These bacteria require a few minerals, so make sure the GH and KH is at least 3 German degrees of hardness. They grow best when the pH is in the 7s. Good water movement, fairly warm (mid to upper 70sF), no antibiotics or other toxins.
2) (Optional)Add some source of the bacteria. Used filter media from a cycled tank is best, gravel or some decorations or a few plants... even some water, though this is the poorest source of the beneficial bacteria.
Bacteria in a bottle can be a source of these bacteria, but make sure you are getting Nitrospiros spp of bacteria. All other ‘bacteria in a bottle’ products have the wrong bacteria. (This step is optional. The proper bacteria will find the tank even if you make no effort to add them). Live plants may bring in these bacteria on their leaves and stems.
3) Add ammonia until the test reads 5 ppm. This is the non-sudsing, no surfactants, no-fragrance-added ammonia that is often found in a hardware store, discount stores, and sometimes in a grocery store. The concentration of ammonia may not be the same in all bottles. Try adding 5 drops per 10 gallons, then allowing the filter to circulate for about an hour, then test. If the reading isn't up to 5 ppm, add a few more drops and test again. (Example, if your test reads only 2 ppm, then add another 5 drops) Some ammonia is such a weak dilution you may need to add several ounces to get a reading.
4) Test for ammonia daily, and add enough to keep the reading at 5 ppm. You probably will not have to add much, if any, in the first few days, unless you added a good amount of bacteria to jump start the cycle.
5) Several days after you start, begin testing for nitrites. When the nitrites show up, reduce the amount of ammonia you add so the test shows 3ppm. (Add only half as much ammonia as you were adding in part 4) Add this reduced amount daily from now until the tank is cycled.
If the nitrites get too high (over 5 ppm), do a water change. The bacteria growth is slowed because of the high nitrites. Reducing the level of ammonia to 3 ppm should prevent the nitrite from getting over 5 ppm.
6) Continue testing, and adding ammonia daily. The nitrates will likely show up about 2 weeks after you started. Keep monitoring, and watch for 0 ppm ammonia, 0 ppm nitrite and rising nitrates.
7) Once the 0 ppm ammonia and nitrites shows up it may bounce around a little bit for a day or two. Be patient. Keep adding the ammonia; keep testing ammonia, nitrite and nitrate.
When it seems done you can challenge the system by adding more than a regular dose of ammonia, and the bacteria should be able to remove the ammonia and nitrite by the next day.
If you will not be adding fish right away continue to add the ammonia to keep the bacteria fed.
8) When you are ready to add the fish, do at least one water change, and it may take a couple of them, to reduce the nitrate to safe levels (as low as possible, certainly below 10 ppm) I have seen nitrate approaching 200 ppm by the end of this fishless cycle in a non-planted tank.
9) You can plant a tank that is being cycled this way at any point during the process. If you plant early, the plants will be well rooted, and better able to handle the disruption of the water change.
Yes, the plants will use some of the ammonia and the nitrates. They are part of the nitrogen handling system, part of the biofilter, they are working for you. Some plants do not like high ammonia, though. If a certain plant dies, remove it, and only replace it after the cycle is done.
10) The fishless cycle can also be used when you are still working out the details of lighting, plants and other things. If you change the filter, make sure you keep the old media for several weeks or a month. Most of the bacteria have been growing in this media (sponges, floss etc).