So I'm able to apply coupons on the Checkout page. Quantity-based discounts also appear on the Checkout page. As does basic state-based Sales tax. But, when you continue from there, you select a shipping service, and then continue to Checkout review. At this point, the coupon is gone, as are the discounts and tax.
The coupon entered still appears in the form, but the Granted Amount is now $0.00.
I'm losing my mind on this one because I'm dealing with a site that is (was) 95% complete when this started happening. I must have introduced something stupid along the way.