I thought that government travel generally allowed business class for trips over eight hours? A while ago, there were tales of government travelers deliberately booking connections to get their TATL trips up to the eight hour threshold.

Government travel frequently books into fairly high fare classes. It might not be prohibitively expensive for the OP to buy up to business class. This should be compared to the cost of purchasing Y+ seats for this route.

OP should note that seat maps aren't good indicators of availability, especially for international flights. also, unless coach is overbooked, UA will NOT do OPUPs (upgrade people for free in this case) and even if there are OPUPs, they will NOT be given to someone without status traveling on less than a full Y fare.