Let's not fall into the trap of seeing this as an XY problem. XY just indicates that we have failed to find common ground in resolving the issue; XY is a sign that each party is retreating to their side for convenience sake - a classic cop out. You are trying to be kind to your plants and use up kitchen scraps responsibly - this is laudable, and we can help in that endeavour. The issues might be: creating the compost, drainage, and annual processing.
For drainage, adding sand to clay can help as long as the mix is kept moist. If clay, with or without sand, becomes dry it can become very hard and is extremely difficult to re-wet. In this sense it can become like cement, but cement is a quite different process whereby a chemical process is forced on a mineral substance to make it temporarily powdery, a process that slowly reverses itself when made wet. Sand can help re-wet a hard soil if thoroughly mixed in. And some clay is good for plants since it binds very well to nutrients and allows root hairs to access those nutrients.
Compost helps prevent hardening soils by keeping channels open in the soil for water to both flow through and be kept available to the plant at the same time as air pockets. So in that sense compost is better than sand to open up a clay soil, but the compost itself burns up quickly and needs to be constantly replaced.
Your current method for creating a useful product for plants is producing an anaerobic product, humus. While humus can be helpful in the very long term, what is needed for your plants in this case is compost, an aerobic product, and they are different. It sounds like your process is handling too much wet material and there is no way the excess moisture can escape. So we need to find a way of reducing that wetness, perhaps by adding dry material like shredded newspaper or wood dust, small chips, chopped straw, dry leaves, shavings that can absorb the excess water.
Thorough mixing of the components not only gets air into the mixture as it decomposes, it also allows you to see if it is yucky and smelly or not. There is a fine balance to be maintained, you may need to add more dry material or even water from time to time. Worm composting is instructive since worms will tell you if the mix is too wet or too dry.
Reprocessing your scraps through compost really requires making the compost and mixing in with your soils at the beginning of the season, planting up your pots and allowing the annual plants and soil to return to the composting process at the end of the year. This ensures that balcony plants are sitting in fresh compost every year. Long term plants need to go into larger pots with more of your soil+compost each year.
The result should be compost used up, good pot drainage and healthy plants.
