Well with this being casual (meaning you don't plan on going fully competitive with it) and your forms of asking for help being a bit too general (I don't have any clue what you're having problems with) all I can do is make some card suggestions.

a couple more land would allow you more consistent mana, also a bit of mana flooding works out with Armored Ascension maybe go with a couple of Emeria, The Sky Ruin so you can have more gas in the late game.

Precinct Captain makes more tokens and has first strike!

Dryad Militant is an upgraded Elite Vanguard , also War Falcon is another aggressive, soldier based creature.

Finally I'd suggest a full 4 Honor of the Pure as they are by far the best card in the deck allowing your large number of small soldiers be able to take your opponent's life total down in rapid chunks rather than bit by bit.

I love the idea of the Precinct Captain and the Dryad Militant

And yes, I do need more Honor of the Pure

The main problem I seem to be having is my opponents simply getting too far in the early game with their green-ramp decks

I would also suggest Ballyrush Banneret in place of Palace guard, and maybe some of the soldier tribal equipment and cards.

card:Gideon's Avenger gets +1+1 every time an opponent taps a creature. card:Gideon's Lawkeeper can help. Don't want to throw you too off course but its an idea.

I never liked the card:Gideon's Lawkeeper... It always slowed me down (i try to go all out attack or force the opponent into stall with killing blockers)

Also i will take a look at the Ballyrush Banneret