I'd say use Temple+Catapult to trash down quickly, get a bunch of Archive/Chariot Race, a single Gladiator, try to get Fortune when you can, and pursue Castles - Archive lets you get decently big hands, so get Opulent Castle when you can. Ignore Palace, it's more important to be thin. I'd tentatively ignore Legionary, as Catapult's attack is stronger here and you want one anyway.
Thanks for the response.
Catapult's attack is stronger than Legionary: Assuming we can rank card goodness linearly, they would discard their two worst cards to Catapult, and do the same to Legionary but also cycle their median card. Probably the median card is average, so it's as good as what they'll draw—but it's harder to plan what to do when you have two chosen cards and a random vs. three chosen cards. I think this slightly favors Legionary. Also, eventually you will have trashed all the treasures you want to trash, and Legionary doesn't require any fuel, so maybe you transition to Legionary in the late game—after trashing and getting a Fortune? I have a hard time seeing cursing as relevant, since there is plenty of trashing. I mean sure, it takes up terminal space, but it eats your Silver. I guess maybe, if you have $3 spare above your main buy... ?
Ignore palace because it's more important to be thin: each use of palace is card-count neutral, but adding cards to be ritual'ed isn't, and staying on top of trashing is at the expense of attacking with Catapult (or digging with Gladiator). I take it this is what you have in mind, approximately? I was tired when I wrote this, I read "Palace" and thought "Ritual". Pedantic nitpicking: I think the goodness of being thin is non-independent of what else you're doing, so "being thin is more important" should probably be recast as "The palace-focused strategy is weaker than some other strategy which performs best when your deck is thin, hence you should thin down, ignore Palace, and do that other strategy", with which I agree. (On some boards Gardens rush beats Palace BM/slog, so thinness is not always good and is not the only argument against Palace.)
Get a bunch of Archive/Chariot Race: do you get as many Archives as you can here, or is a small handful enough? In my experience, decks similar to what you describe work ok-ish with 3-4 Archives; they would probably work better with 1 or 2 more, but the opportunity cost is often a Gold, so you're drawing a bigger proportion of a smaller total payload. Eh, if I replay this board I should probably try with more Archives just to compare. How big a deal is Chariot Race? It looks to me like it can safely be skipped in favor of more Silver.
I take it Wild Hunt and Royal Blacksmith are out of question in this deck: you have plenty of actions and few terminals, so there'll be a lot of dead draw and the cards will prove not worthwhile. Maybe Overlord could play here? It can trash your Catapult/Temple/Gladiator once you don't need those, then become a spare Archive or Legionary? (Or maybe Catapult if that's better.) The cost looks non-trivial, though.
How big a deal is Fortune? Clearly Fortune is a good card—but you can get it if your opponent goes for Gladiator even if you don't. If you pick up a Gladiator and your opponent doesn't, your advantage is a cheap terminal sometimes-Gold (esp. if paired with a Castle in a 2p game), you gain a Gold when you buy your Fortune, and you likely get to play yours first (assuming you have $8 when you uncover it). The cost of this is a large amount of terminal space used on playing Gladiator that could be spent either trashing or attacking with Legionary. Is that worth it? Maybe the right timing of Fortune (if you have the only Gladiator) is such that you're likely to drain the last two provinces from the supply on your first Fortune turn—that way you try to maximize the value of the asymmetric benefits of uncovering Fortune.
I think you want to do the catapult thing.
Boss the Catapult split, pelt them with Rocks, then pelt them with a few Catapults once you have completed the bombardment?