I recently did a small experiment of my own that's distantly related to what you're proposing to try. Can't hurt to tell you what I did, might be of some small use to you.
I have 3 Betta fish, each in a 2.5 G tank. I used to keep them bare, with nothing in the tank other than the fish. Typically I'd perform a partial water change, [ PWC ] biweekly, during which I siphoned all fish waste from the bottom. Uneaten food would be removed daily.
But I added a fair number of plants, because I didn't care for the bare tanks. After they'd been growing for awhile, I became curious about what effect, if any, the presence of the plants might be having on the water parameters. To find out, I stopped doing water changes about ten days ago. Instead, I only replaced [ topped up] evaporated water.
Each 2.5 G tank has one full grown Betta. Each has 2-3 stems of Hygro difformis, kept from floating by small weights; a small mass of loose Java moss; 2-3 mesh grown patches of fissidens moss; 2-3 quite small anubias plants, with 2-3 rooting leaf cuttings of the difformis floating on the top. Bottoms are bare glass, but have a large Indian Almond leaf plus a couple of cured brown oak leaves resting on the bottom, to add tannins and humic acids to the water. There's a fan that blows on the surface of the water if needed to control temperatures.
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There is no filtration of any kind; no powered circulation of the water. Water only moves if the fish do & perhaps with plant respiration, and perhaps some if the cooling fan is running. Lighting is provided by round 8" reflectors [ utility lamp], with spiral 6500 K bulbs in them, 9W. The reflectors sit on the tank rims. One pair of tanks are side by side and share a lamp. The other has its own lamp.
I tested the water every couple of days, as I had no wish to risk the health of the fish. I never had any detectable ammonia. Ammonia is the most common by product of fish waste, from fish urine mainly, but it can also come from decaying food & other organics.
In tanks with filtration that are cycled, nitrifying bacteria in the filters convert this ammonia to nitrite, then other types of nitrifying bacteria convert that to nitrate. Nitrate is controlled in part by plant uptake and in part by PWCs.
Today was my tenth day in, and test results were; Ammonia 0, Nitrite 0 and Nitrate <10 ppm. That was quite surprising, as I had expected to see at least some ammonia. The only conclusion I can make so far is that the plants are directly consuming the ammonia output of the fish. I have wondered if the nitrates indicate that at least some nitrifying bacteria are at work too, but since I do add minute amounts of fertilizer for the plants, that may be the source of nitrate.
I'm continuing to monitor to see how long the water quality remains acceptable. The only thing I add to these tanks is top up water, food for the fish, a minute amount of liquid fertilizer twice a week, and Excel, a carbon source for the plants. I add the last two because I want the plants to grow as well as possible. So each tank is dosed with 3 drops of API's carbon source daily, and just 1 drop of Flourish liquid fertilizer, 2-3 x week. Timers control the light cycle, which is 12 on/12 off. Despite the long photoperiod, there's been no algae growth, and they've been lighted this way all summer.
Of course, these tanks are not closed systems such as you're proposing. They also have a much larger water volume & substantially greater surface area where gas exchange can happen. So no stagnation has occurred, fish are happy and healthy. I feed them live food 3 or 4 days weekly, other days it's frozen food, and I skip feeding one or two days weekly. Feeding once daily only. Anything fed live that is missed will be eaten later on, and meantime survive and have no effect on the water quality.
I plan to carry on with my little experiment to see how long the water remains in acceptable condition without water changes. I hoped the results might be somewhat helpful to you. They certainly have made it clear to me that with this plant load, I don't have to do nearly as frequent PWCs as I used to do.
, small snails, about 1-2 inches of sand/rock mixture in the bottom, and then leaf debris. My first concern is that there will not be enough space for said guppy to do his "thing" whatever that may be with fish. second, I can't seem to get any of the Elodea or snails (where would I get these?) The whole point of this is to create a closed and self sustaining ecosystem. I could really use some help. 
