Hey,,
those white bugs you have are probly the same as the ones I get after prolonged damp soil. I use cold pressed(cause the heat pressed/extractions take away the active stuff in the neem,) NEEM Oil,
there are loads of brands,,Enistien oil is one,,,and neems really good at controling spider mites but helps to kill all bugs. Used as a soil drench it will fuck up the life cycle of the bugs but will fuck up all bugs,,benificals too,
but what I do to get the wee white maggot with legs bug(havnt seen a problem from them I just dont like them) I let the soil dry out,,after a good water,, and place a small tray with water in it(its the bacon fat tray from my G.Forman Grill) and place this in the grow room between the pots, and add one drop of bleach or any house hold cleaner,,somthing that kills anything so bleach is great for that,, and the wee white bugs jump from the pots which are dry into the water and then die from the bleach,,first time I did it with just a tray of water and it was full of these bugs,dropped abit of bleach into it and they all died...haha, so now if I see them after I have watered I just add the 'tray of death' to the flowering room and they all launch themselves into it. Its very effective and means you dont have to add pesticide to the pot,,. so yeah let the soil dry and they will migrate to the water....
Take it easy...o P.S. Im organic too so I understand you dont want to add man made chemicals...take it easy