Sorry, just took a look at inventory. 6am LAX-EWR on 3/28 looks fairly promising: booked 17/28, J9 D9 Z8 P0, and pretty light in E+. Better stil, unlike SFO which has seen big capacity cuts on early-morning transcon capacity, there are three LAX-EWR between 6 and 8am. P0 is a bad sign, in that they think they can sell relatively pricier fares, but at least keeps those discount buyers out of your J cabin.
Odds maybe ~30-40%? PS can be very volatile, so you might end up clearing very easily or missing by a mile, but you stand a shot.
9pm EWR-LHR on 4/2 looks excellent for you -- 13/39 is a great filled-to-unfilled ratio, P9 is as good a sign as you typically see before T-2 weeks on EWR<>LHR, and Monday nights are pretty quiet. Probably 80-90%, unless something irrops/event-related happens to cause a sudden spike in J demand on that flight. Nonzero chance you clear some time (like days) before departure, in whcih case get 1A or 1L
It's possible phone agent was being truthful/accurate, but I've heard so many different stories that I would take any pre-check-in upgrade list status with a giant pinch of salt.