Actually, in many cases it will be substantially cheaper to upgrade the entire route than to upgrade an individual segment. The exception, as WineCountryUA notes, are the online offers that may appear during the purchase process and again during check-in.

Unless you have an exceptionally expensive economy class ticket (for example, a fully refundable or unrestricted ticket), $860 seems like a pretty low buy-up offer. A miles + cash upgrade from deep discount coach would cost $600 plus 30K miles (in one direction). Although it's always possible, personally, I wouldn't bank on finding a much better price.