3 inches should be more than enough. You want it deep so that the lowest level of substrate becomes oxygen deprived, supporting only the growth of anaerobic bacteria which convert nitrates to nitrogen gas. When you see little bubbles/gas pockets forming in your substrate, those are nitrogen bubbles, and your anaerobic bacteria are doing the job. Aerobic bacteria in the upper layers of your substrate convert ammonia to nitrites, and nitrates to nitrates.
Do not stir the sand. That would only supply oxygen to the bottom layer, killing the anerobic bacteria and eliminating the substrate's ability to remove nitrates from your system.
You might also add macroalgae (Chaetomorpha is my preferred choice), which will absorb nitrates from the water (phosphates too) as nutrients for growth. When the algae gets overgrown, you just toss some of it away or pass it on to a needy club member who is setting up a refugium.
By the way, I have plenty of free Chaetomorpha.
Jay