Thanks for the invitation to look at your proposal and comment. I've researched certain of these aspects exhaustively, but I still have more questions than answers myself! According to my findings, my humble opinions, and some of my suspicions as well -
I suspect the water chemistry is actually more complex than we usually get into discussing or fully understand in the hobby. Looking just at nitrates is overly simplistic perhaps, and I suspect there are a great many more complex organic molecules present, and some of which can take time to properly break down, oxidize, reduce, etc. I'm not sure however if bacteria or plants are better at dealing with these. And it depends upon how natural of a planted tank you might want to go.
Personally, I'd hedge your bets and try a multi-faceted approach. But still, to maintain water quality, it shouldn't hurt to use ozone and/or activated carbon. Those will, respectively, chemically reduce the organic compounds to a form which plants can absorb, or just remove them, instead of having those complex molecules building up in the tank.
I tried to read into it, and as a result don't believe in discus growth-inhibiting hormones. Nitrates, and potentially other parameters I believe can inhibit growth though.
For a deep sand bed, I'd suggest sand with a little larger grain than play sand as you don't want to stop all water infiltration. Depending on if you want it light or dark, I'd suggest pool filter sand or like a relatively fine Black Diamond blasting sand.
If you have burrowing fish like rays, I would separate the soil base from the capping sand with large sheets of rigid plastic knitting mesh, with say a half-inch of sand underneath that. The plants will be able to root through it, and won't get uprooted as easily. Your plant roots should help keep the substrate healthy. Malaysian trumpet snails are supposed to help with that as well. And I thought of even trying to introduce live blackworms, similar to how reefer's depend upon worms in their substrate to keep it aerated and healthy, though I'm a bit nervous about that. (Whether keeping a ray negates all that, I have no idea).
I don't know anything about kitty litter, but would personally prefer a mineralized topsoil base, supplemented with granular dolomite, potash, powdered clay, etc. The granular dolomite should help keep the substrate from acidifying over time, which would otherwise halt bacterial activity.
Basically, to have healthy plants, a healthy tank, healthy fish, and little algae, you want to make sure the plants have as much in terms of nutrients as they can get, while the algae does not. Therefore, if you keep the nutrients under the sand, where the plants can reach them via their roots, but where it stays mostly out of the water column, then you'll have good healthy plants, little algae, and won't need to worry really about dosing nutrients in the water column daily.
I suspect that even to keep healthy softwater fish, you want an appropriate blend of minerals in the water, (just like a reef tank), but only in much smaller amounts, including calcium, magnesium, and alkalinity. If you're not doing regular water changes, then your hardness could get depleted as organic acids produced in the system neutralizes it, causing your ph to drop which could kill your biofilter, aka old tank syndrome. I don't know what your tapwater is like, but mine is rubbish and I wouldn't want to use it directly. You could use RODI water and then remineralize it with discus buffer or similar products. That could be in your water-change water or perhaps even your top-off water, but you would want to test and monitor those parameters. You could have a bag of crushed coral and dolomite in the sump or filter, which might melt to remineralize the tank as necessary and gradually. Or, it might get covered in bacterial bio-film, and quickly stop releasing minerals. Either way, you should keep an eye on your hardness and TDS, to make sure it doesn't get out of hand.
I'd want to do DIY LED lighting myself, but if cost is paramount, then I believe that a few rows of florescent lights might be your cheapest option in terms of initial upfront price. You can also buy LED tile fixtures relatively cheap from China on auction sites nowadays, which do the job. I'm thinking that natural white LED's which are around 5000K give the best looking light and fullest spectrum for a planted tank. And if you can get a supplemental RGB strip light, then the three of those specific colours will supplement some of the gaps in the spectrum of white LED's, (such as the green specifically), while contributing a white-ish light themselves. I haven't done it yet myself, but I believe the combination should give the most natural full-spectrum look, and if the RGB strips are tune-able and dimmable, then all the better.
I haven't thought at all about what sort of lumen you'd want to try to achieve, but I think with what you're talking about, you would be underpowered. You can have glass/plastic closing off the top of your tank, with the lighting just on or above that, which is what I have in my reef tank as well. Four LED tile fixtures as necessary for an 8' tank aren't going to be cheap regardless though.
To maintain ecological balance, you may want to look at it as having to have your light intensity and plant growth at least equal to the metabolic output of your livestock. For that reason, I wanted to have relatively intense lighting (but adjustable), and then have fast-growing floating plants. They'd shade the tank, mop up any nutrients in the water, and then I could net out half of them each week to serve as a nutrient export mechanism. If you have a sump you could do the same thing there, with different types of plants as well. Floating plants or emergent plants in sump, which can consume atmospheric CO2 would really help scrub your water in a non-limiting manner, if your tank doesn't have pressurized CO2.
I'd do a dry start as well, to get the plants rooted and give them the upper hand over algae before you submerge them. You may then not need many algae eaters with sufficient plant growth. I like nerite snails, and I think apple snails are good as well, as they can consume and therefore recycle the cellulose in dead plant leaves. Plecos get mixed reviews, but I think bristlenose might be most suitable for you.
I guess for heating you'll likely need at least two 300 watt heaters, with the redundancy there for safety.
If you have a large enough mattenfilter area, such as using it to separate sump compartments, then it shouldn't clog too quickly, or at most should be designed to flow over the top if clogged and needing to be rinsed.
I would perhaps suggest using more water current than most discus keepers use, so long as the fish aren't struggling too much. That should help keep the tank, the plants, and the fish healthy. Depending upon your approach that topic is a little tricky, as fish and bacteria do best in well oxygenated water, but that might push some of the co2 out as well then. A powerhead in the tank causing water ripples across the surface would achieve the necessary oxygenation. If you have sufficiently intense lighting, then the plants should produce oxygen, though you don't want the levels swinging either from day to night. If you're using a sump in the stand, then you could light the fuge/sump on a reverse cycle? Some might suggest keeping the tank tightly covered to keep in CO2. I'm rather split on this issue, as I suspect poor oxygenation can help pathogens thrive.
With discus, perhaps stay away from some of the deeply inbred domestic strains, and find wild strains which are a few F-generations into being tank-bred. Or a wild/domestic cross perhaps.
There are threads in various places giving lists of plants that thrive in the mid-80's temperatures in discus tanks. Have a search for those.
If I recall correctly, 4 discus is too few, and for hierarchy/aggression issues, you're better sticking with at least six.
I hear beefheart is too messy though for a planted tank, as too much of it is left in the water for even fast-growing plants to keep up with. And you might not be able to feed as much as some discus enthusiasts do. While if you were doing multiple daily water changes then it wouldn't be detrimental to constantly overfeed your tank in order to max out their growth.
And do first read Ecology of the Planted Aquarium, but Diana Walstad. But take it with a grain of salt and with the view that you can hybridize that approach still, IMHO.
Best of luck, but approach it cautiously and thoughtfully!