The studies that properly identified the nitrifying bacteria in aquariums are fine resources, and you are doing OK so far. Sure, more studies have been done on waste water plants, but those conditions are not exactly the same as aquariums. Many similarities, but some differences, too.
Dr. Tim's One and Only, Tetra Safe Start, Microbe Lift's Nite Out II and probably some others are good sources of the right species of bacteria. Look for Nitrospira species of bacteria, as you did. Absolutely there are other species that have been properly identified, and are included in the bottles, but Nitrospira is the key to having found a bottle with the right species. Some bottle with the 'wrong' species still have the same genus of bacteria, just the wrong species.
I would not increase the temperature beyond what the plants will handle. Mid to upper 70s is just fine.
Ignore the cloudy water, there are many species of bacteria getting going in the tank, and cloudy water is often caused by the growth of heterotrophic bacteria. Not nitrogen cycle bacteria, but beneficial in other ways. They will settle down.
If you had no plants, then it is OK to turn off the light. But keep the plants happy with the right level of light. It is not a problem at all to slowly stock the tank with plants. Just keep on feeding the bacteria. Some plants do not like a lot of ammonia, though. If you see any burn on the plants you might try dosing ammonia to only 1 ppm in the AM then 1 ppm in the PM. This will keep the maximum ammonia low enough (1ppm) for pretty much all plants, yet still keep on feeding the bacteria.
You are right that watts per gallon is not really the key anymore, especially with LED lights. Do you have access to any sort of light meter? I understand there are ways to convert some photography meter readings to PAR.