ABZAN SIEGE DECK LIST
Lands (26)
6 Forest
7 Swamp
8 Plains
1 Scoured Barrens
2 Sandsteppe Citadel
1 Jungle Hollow
1 Blossoming Sands
Creatures (23)
1 Mer-ek Nightblade
1 Carnivorous Moss-beast
1 Ivorytusk Fortress
1 Armament Corps
2 Longshot Squad
2 Disowned Ancestor
3 Ainok Bond-kin
1 Sungrace Pegasus
2 Child Of Night
2 Abzan Falconer
2 Tuskguard Captain
1 Abzan Battle Priest
1 High Sentinels Of Arashin
1 Razorfoot Griffin
2 Salt Road Patrol
Other spells (11)
1 Incremental Growth
1 Flesh To Dust
1 Hunt The Weak
1 Dragonscale Boon
1 Abzan Charm
2 Kill Shot
2 Abzan Banner
1 Eternal Thirst
1 Suspension Field
Obviously, the Carnivorous Moss-Beast is the first thing to go. Mer-ek Nightblade and Longshot Squad are outclassed by what the Abzan Falconer and Tuskguard Captains provide at lower mana costs. Flying and Trample are always more relevant than Deathtouch and Reach. Salt Road Patrols should go for more copies of Abzan Battle Priest. You definitely want more copies of High Sentinels of Arashin, too.
I think Outlast, even though it's a bit of a slow mechanic that can only be activated at sorcery speed, can work okay in Limited. It's much harder for it to work well in Constructed, as if you go to activate one of your Outlast abilities, they'll probably kill your creature before it has a chance to do much damage. Unchecked, though, Outlast creatures that give your creatures with +1/+1 counters extra abilities can win you the game, especially as they have a Prophet of Kruphix-lite to assist them.
You would definitely want to run at least a couple of copies of Abzan Ascendancy in the deck, which puts a +1/+1 counter on each creature you control when it enters the battlefield. Plus, when any of your nontoken creatures die, you get a 1/1 flying Spirit token. If there's anyway to make this deck better, it's that.
If you want to start from complete scratch, and don't want to invest in the mana base, I think you're best off looking to Theros block's Heroic creatures that gain +1/+1 counters from their Heroic triggers. Cards like Lagonna Band Trailblazer, Hero of Iroas, and Fabled Hero coupled with High Sentinels of Arashin and perhaps a couple of Abzan Falconers, you're looking at a pretty solid mono-white deck. Is it top-tier? No, but that's one way you could go for not a ton of money.