Here are my recommendations:
You will need artificial light. The plants won't be able to photosynthesize properly with window light alone, which will keep them from absorbing ammonia at the rate you need to keep the colony of inverts and two fish healthy. Shoot for around 2 wpg in addition to natural light. Set the lights on a timer for 5 hours on, 4 hours off then 5 hours back on. This will cut down on algae and allow for more CO2 production for your plants.
Plant lots and lots of plants. You want the tank to nearly be choked with plants, and I don't mean moss. Use plants that don't need a lot of pruning, like rosette plants, plants with rhisomes and plants that send out runners. Stay away from stem plants. Go for plants with low to medium light requirements and especially look for plants that can get their carbon from calcium carbonate as well as dissolved CO2. Plant everything at once so you don't have algae problems. I hope you have a friend who can help you with this because otherwise you're looking at spending at least $100-$200 on plants.
You want some plants that use CO2 from the air to export nutrients but you don't want to use willow branches. Willow trees suck nutrients like nothing else and will starve off all other plants in the tank. You don't want to create the same set up as a mangrove refuge because you have a different goal. Instead, use floating plants and submerged plants with emergent growth to export some but not all nutrients. Remove the floating plants as often as needed to keep the light level adequate.
Use organic potting or top soil as your substrate, about one inch covered with 1-2 inches of fine gravel or course sand. Don't add clay or peat because they will lead to an abundance of iron that will give you bad algae problems which may end up killing your plants and fouling the water. Get something with calcium, like oyster grit or crushed cuttle bone, and sprinkle several handfuls over the soil before capping it with gravel. This will make sure your water hardness isn't depleted by lack of water changes or the use of rainwater.
The organics will not cause the soil to "rot" but it will become partially anoxic. That is okay as long as the substrate is not too deep. If it's too deep, say 4 inches deep, you could have troubles with hydrogen sulfide. This is why I don't recommend doing the substrate incline as you described.
Cherry shrimp don't reproduce fast enough for your needs. They also need food and algae alone won't be enough if you set up the tank right. Use scuds instead. They reproduce very quickly and are happy eating detritus. They also hide in the substrate so the fish won't be able to gorge on them all at once.
Make sure you get sub-tropical omnivorous fish, something that can snack on algae but survive on scuds and not mind the lack of a heater. A few North American native livebearers would be ideal. I don't recommend hatching killifish eggs for this because you need healthy adult fish that can handle less than ideal conditions. You want to get fish that do not have an upturned mouth. Those fish naturally look for food at the surface of the water, which they won't find here. You want something that knows to poke around the substrate while looking for food.
If you're going to go through with this project don't let the expense of something stop you from buying it. The reason no one does this is because animal cruelty is a real issue. I do believe it's possible to successfully complete this project for short time but you really need to understand the water chemistry issues involved. I would never, ever make a fish live out its entire life cycle in a stagnant box of water. That's why I recommend livebearers. Let them have their first brood then do a water change and add a powerhead for some water movement. Once you get the powerhead in there the tank might actually become self-sustaining.
