Can I attach Warmog's Armour to an unbuffed unit, conquer Monastery of Hirana, and sequence the two conquer triggers so the unit gains a buff from Warmog's first, then spend it with Monastery to draw 1?

No. Under the Unleashed rules update, "may" triggered abilities with costs within instructions (like Monastery of Hirana's "spend a buff to draw 1") require you to pay the cost when placing the ability on the chain, not when it resolves. At the time of conquering, your unit doesn't have a buff yet (Warmog's Armour hasn't resolved), so you cannot put Monastery's triggered conquer ability onto the chain at all. You can no longer sequence these triggers to get both effects.