Having reviewed your information and photos, my initial thought is that there are insufficient nutrients. I'll explain; some of this you may already know, but I don't know if you do or not, so I will be detailed so it is clear.
Plants grow by photosynthesis, and to photosynthesize they need light and 17 nutrients. Provided all are present, plants will photosynthesize to the max. But as soon as something is no longer available, photosynthesis slows or may stop altogether. This is called the law of minimum. The limiting factor in an aquarium should always be the light.
You have plenty of light, perhaps too much, but you also have CO2 diffusion. But without the other 16 nutrients, plants can't make use of all that light and the CO2. This is what is wrong with the moss I believe, there is too much light (moss prefers less light) with insufficient nutrients.
Some nutrients occur naturally in the aquarium, especially with fish. Nitrogen is a major nutrient, which plants prefer in the form of ammonium which comes from the ammonia released by fish and bacterial processes in the substrate that break down organics. Oxygen and hydrogen (water) obviously occur naturally.
Some nutrients enter via fish food, and will usually end up in the organics in the substrate. Some enter via the water, such as calcium, magnesium, zinc, nickel, iron, manganese, sulfur, etc; but depending how many of each of these is in the tap water, the amount actually available for plants can be quite limited.
In a natural or low-tech system, with no added CO2 [which in such a system occurs naturally from fish respiration and even more from the decomposition of organics in the substrate], it may or may not be necessary to add nutrients in the form of fertilizers. Substrate (root) tabs may be sufficient, but some plants may not benefit if they are not rooted in the substrate. A liquid fertilizer that is complete is usually sufficient. Something like Flourish Comprehensive Supplement, which is my choice. Plant growth in such a natural system will be slower, but still steady.
Once you up the light intensity and add diffused CO2, the need for the other nutrients increases considerably, and sufficient will never be available without increased supplementation. High-tech systems often add nutrients daily, either as liquid preparations or using dry fertilizers that the aquarist mixes with water. Without this, the plants will struggle, as they are here. Root tabs usually are insufficient in themselves, since they, like many liquid fertilizer preparations, are basically intended to supplement natural systems that just need some boosting, so to speak.
You have two choices. One is to remove the CO2 and reduce the light, and switch to a more natural system. The other is to retain the light and CO2 but add daily nutrient supplements.
My approach has always been natural or low-tech, so if you want to go that route, I would be happy to guide you; the photos of my tanks [under "Aquariums" below my name on the left] illustrate this approach, which I find sufficient for my needs. I've no direct experience with the high-tech approach, but we have other members who have, and they will be able to suggest feasible fertilization schemes to balance.
Byron.