I use Bti, there is a product called Gnatrol which is organic-certified BTI powder, it's very effective against the gnats. Mosquito dunks are the same thing, not OMRI-certified but basically organic. I would grind them into small particles and let them sit in water for a while before watering, and then let the pieces fall into the soil as you water. Usually I only have to water 2-3 times with Gnatrol and they're gone.
I'm intrigued by neem meal, definitely want to try it. An organic fertilizer that also stops the gnats? that would be cool! I use "Eintstein's Oil" a neem-based product, as Lotus said it's great for foliar spray during veg for many insect pests, including spider mites. Using it for soil-drench will kill all the gnats but it hurts the plants.
D-earth is great for gnats, but it has to be dry to work. If you wait until the top soil surface is dried out, you can dust it over with DE and watch as the gnats struggle and die! However as soon as you water it stops working. Mixing it into the soil doesn't work. Dusting the trays under the plants also helps, kills the fuckers when they crawl out, but again as soon as you water it stops working.