Great wrap up on denitrification Bfrench!
Ideal DSBs are at minimum 4" but I believe 6" is ideal. The less you disturb the lower layers, the better it will perform.
The main methods of removing nitrates are macro algae, algae turf scrubbers, carbon dosing (biopellets, vodka, vinegar, etc), sulphur denitators, and regular water changes. I personally employ biopellets combined with a large skimmer. Keep in mind for water changes, nitrate removal is directly proportional to the percent of water removed. If you do a 50% water change, you will have reduced your nitrate level 50% as well. Please don't go out and do 50% water changes. [emoji4]
Shallow sandbeds give you more surface area to perform nitrification, an aerobic process that converts ammonia/nitrite to nitrate. Otherwise, it's there only for aesthetics and a refuge for sand dwelling creatures such as pods and also for certain species of wrasses to sleep in at night.
If you use aragonite sand, it can act as a calcium buffer in the more acidic zones of the sandbed.
The eggcrate is just personal preference whether you feel it'll have any impact in your system. If you go the route of a DSB, it may be a moot point.