Which flights are you considering?
On UA1003 on 3/22, there are 5 banks of 3 open seats in E+, in addition to another three sets in E- (way back in rows 51-53).
On UA2 on 3/31, there are 6 banks of 3 open seats in E+, in addition to another three sets in E-, again in the back of the plane.
Can't help with any "secrets" to a good last-minute fare. It's spring break season.