If something goes wrong with your inbound flight (i.e. it's delayed, canceled, etc.), you'll want to try to stick to UA metal if possible. If you buy a separate ORD>BNA on AA and something happens on your UA flight, you're screwed. I'd do the IAD-BNA for that reason alone. Even then they don't have to help you, but UA would be much more likely to in that situation as they would have control over both reservations.

Also, book the onward IAD-BNA next day award flight anyway (even if you buy a ticket for the night before also). No reason not to - it's the same price. It then preserves you that as an option were something to go wrong - so you're double covered in a worst case scenario.