Welcome to TFF.
There is a lot of misunderstaning in this hobby about filtration. The short answer to your question is yes and no. It depends upon the specifics of the aquarium, and each aquarium can be quite different biologically, even if we use the same substrate, light, fish load, feeding, plants, etc. I have 8 tanks running in my fish room, and each is certainly unique biologically.
It is possible to have a healthy planted tank with no filter at all. I've done it, as have others. You must have a specific balance between fish and plants for this to work. As soon as you tip the balance--by too many or too large or the wrong combination of fish, too few plants, too slow-growing plants, too much fish food, insufficient water changes--you can have a disaster overnight.
The same thing can happen with a filter too of course, but provided the tank is biologically in balance to begin with, the filter is more of a safe-guard. There is a real myth in the hobby that the larger the filter or the more filters, the better, but this is completely false. The fact is that too much filtration (meaning, with the use of filter equipment) can be detrimental, not beneficial.
I have filters in all my tanks, and all have live plants, and all including floating plants. These floaters are really the key, as they do more to "filter" the water because they are fast growing, and they are fast growing because they have brighter light (being right under the tank lights) and can assimilate CO2 from the air as opposed to solely from the water, and this is about four times faster for the plant. So there is a real benefit to floating plants. Some call them ammonia sinks, because they can assimilate a lot of ammonia/ammonium. Plants take up the ammonia/ammonium faster than the
Nitrosomonas sp. bacteria, so this is another reason why you can do without filters--again providing things are intially in balance.
I also have a filter in all my tanks now; the smaller (10g, 20g, 29g, 33g and 40g) each have a dual sponge filter. The two larger tanks (70g, 90g) have Eheim Pro II canisters. The prime job of all of these in my tanks is one of water cirtculation and clarity; mechanical filtration circulates the water and removes particulate matter. Obviously, all these filters will function as biological filtration too, but I do not rely on them for this. And it is true that in planted tanks, you do not want to be overdoing the biological filtration because the filter is then competing with the plants.
Another aspect of this is that there will be more bacteria elsewhere in the aquarium than in the filter, and primarily in the substrate. The substrate is the most important part of a healthy aquarium. There are many species of bacteria besides the nitrifiers that are important, and all these can be found in a healthy substrate.
So to try and provide a summary answer to your question, I would say a mechanical filter that does not overdo the water movement is advantageous, but biological filtration is not. The latter will occur, but should not be "encouraged."
On your readings, that is what I would expect. As I noted above, plants take up ammonia/ammonium as their preferred source of nitrogen, and when this is insufficient (in balance with other nutrients and light) they will turn to nitrate (possibly nitrite too, though the evidence for this is still scanty). By removing the bacterial filtration that occurs in the filter, you are providing more nutrients for the plants. However, Anubias is slow-growing, so its capacity for helping here is much more limited than is that of the stem plant Ludwigia. Floating plants would significantly increase the safety zone, so to speak. I don't know the fish load (your "heavily stocked" may not be my interpretation of the term) or feeding, but I would assume they are not maxed out, though it may still be early days. But the establishment of the biological system for the several years mentioned likely means you have a good substrate filter bed. In a new tank, something like this might not work at all.
Byron.
