Commerce Coupons, Discounts, and Tax not appearing on Checkout Review page
Solved! Rules was the culprit. By rolling back to the previous stable version, all of the problems with checkout disappeared. Everything applies correctly to the Checkout Page, and is still there when I get to Checkout Review. 

Just to be clear, I replaced the current stable version of Rules (7.x-2.8) from January 2015 with the previous stable version (7.x-2.7) from May 2014.