Hi yonygg,
Did someone check whether in that scenario the new Vmca is still higher than V2 (+10)?
If no body checked and control became a problem then reduce the thrust (to TO Thrust). You can't be any worse off than having an engine failure at V1 and keeping TO Thrust to AA and clean wings.
our E/O recovery wasn't perfect and we didn't meet the planned performance calculation and now our new flight path is lower than the calculated one,
Since you had all engines operating until >800 ft then your flight path must be better than having an engine failure at V1.
and we also deviated 10 degrees off course, and up ahead there are some obstacles or terrain, and the next thing we hear is the GPWS going off and we must add power. Now what?
Display Terrain on your ND, weather on the other. Your enhanced SA should discourage a turn towards terrain.