There are three big reasons why Red is one of the weaker brigades: 1) Lack of effective drawing 2) Lack of CBN battle winners 3) Lack of capture protection. This is why the most effective way to use Red is to have a Teal splash. If you don't want to do that though, then you should definitely add Mustering for War and/or Peter and 4DC (Peter helps vs. TGT decks as well, though he does hurt your Simon). Ram's Horn is also critical, and makes Red's amazing battle winners even better (Freedom! and Trumpet and Sword are arguably among the top negatable good enhancements in the game). The Sabbath is also a good add, as A Soldier's Prayer + The Sabbath allows you to have two shots at perfectly CBN battle winners. Blue Tassels would be a good idea as well, since your defense doesn't depend on capture at all.
As for what to take out, I've never seen Peter's Curse do too much, as it's far too easy to get rid of. You won't need HoH if you add a couple of ways to make your enhancements CBN, as it makes your Centurions less useful. Heldai and Adino typically don't help too much in a pure Red deck, and you can replace Adino's Spear with Warrior's Spear (which can be really annoying to your opponent for a turn or two if you don't have a good offensive setup but you have Spy and WS). David could probably come out as well, as he won't be too useful until August.
Your defense looks pretty solid, except that I've never liked Philly Chariot and Horses in a deck like this. You only have three enhancements that aren't weapons or interrupts anyway, and its pretty easy to get rid of for opponents if they feel threatened by it.
As for where to get Goliath, the only place to get them (aside from Regional tournaments) is probably the Market forum where I've seen them go for $20-$30 usually.