What makes this a speed deck?
Your offense isn't big enough to get 5 souls. Unless I'm missing something, you only have one battlewinner and no way to get it back (Lemuel only searches for O.T. good cards, and his ability doesn't work unless you have a royal female in play, which you don't use in this deck). You'll need to beef it up a lot more.
On defense, you've got way too many enhancements.
Also, there is a Philistine site: Ashdod allows your OT Philistines to use enhancements of any color except orange and pale green (which would be great for this deck).
I'd suggest something like this:
OUT:
Harvest Time
King Saul
Gleaning the Fields - unneeded
Prosperity - unneeded
Asa's Good Reign - unneeded, plus if your opponent bands to a king with this on it, he'll be immune to pretty much your whole defense.
Dance of Death - you shouldn't need more numbers than you already have
Lahmi's Spear - you shouldn't need more numbers
Idle Gossip
Men as Gods
Ishbibenob's Spear
Gifts of the Magi - no way to take advantage of it
Temple of Dagon - not very useful
Burial Shroud - not needed
Site Doubler LS - not useful with only one site which is what I'm suggesting
IN:
Destruction of Nehushtan
Ashdod
King's Daughter
King David (or King Jotham if you don't have him)
Testing Solomon's Wisdom
Royal Parade
Peace Treaty
Glittering Sword
Gomer (Crimson)
Midianite Attack
Philistine Armor Bearer
Go Into Captivity
Priestly Crown
1st Round Protect LS
It's entirely up to you whether follow this all the way, partially, or not at all.