Advise for faster composting new lasagna bed

[Stvrob]

I have a bit of a dilemma. Four weeks ago I started a new lasagna bed for tomato expansion of my garden. It's 18'X 4' x 18" high. The base soil is fine white sand, excessively drained, and likely infested with hungry nematodes. Cardboard base then leaves longleaf pine needles old magnolia and hickory leaves some layers of newspaper plus A few bucketfuls of anerobic kitchen sink waste from where the kitchen sink drains into a nasty pit. Didn't have much green nitrogen waste so I used a few pounds of 10-10-10. It's been very warm weather but it's hardly started cooking, just warm in some places, cold in others. I would really like to set tomatoes out in three weeks. I was thinking of piling on a huge amount of Spanish moss on top mainly to insulate it so it can start cooking. You all think this would work? The weather has suddenly turned cooler with nights in the 30's and highs in the low 60's.
Anyone have any ideas on getting this area ready to plant by Feb 20? I don't have access to any manure, hoping I could just add nitrogen from a bag.