Do not use aquasoil if using soil. For one thing its not needed with soil. For another, aquasoil is very very light and you want the soil to remain very firmly capped. You want to minimize the mess soil makes when you need to pull plants and aquasoil is not ideal. You can if you want, skip soil and just use aquasoil either by itself or capped, but don't mix them together.
I have two tanks with soil in them right now. One is my quarantine tank that has a bare minimum of soil. The other is a proper walstad bowl. (foo the flowerhorn's tanks are all walstad tanks) Here
is a link to the journal if interested.
Anyway in both my soil tanks I am running a 50/50 mix of HTH brand pool filter sand and Safe-t-sorb. Its working quite well.
Regarding your soil turning anaerobic under sand. Well, it will. However, if you plant heavy everywhere you have soil in the tank, the roots of the plants will aerate your soil. This means you won't get buildup of sulfurous gases. Any cap of sufficient depth or fineness will make soil go anaerobic because the soil itself is incredibly fine. Only the roots of plants will keep it/change it to aerobic.
You also might have trouble finding organic choice potting mix as its been discontinued. Fortunately any organic soil will work fine. You will want to use one with the lowest concentrations of nutrients possible. So flip over the bags at your local gardening supply store and find the one with the least nutrients.
I also wouldn't spend a lot of time sifting the soil. Just put in a bucket and then soak it in water. Wait a few hours and then remove anything still floating. This will be about 5/6ths of the "soil" so fill your bucket with that in mind. What sunk to the bottom is your soil for your tank. The stuff that floats will be ground up wood and leaves.
For my tank I did a couple of weeks worth of water changes on my soil while it was in a bucket to get as much nutrient leech as possible. It worked incredibly well but not everyone wants to spend that kind of time so /shrug.