Both pilots should be monitoring the 'plane.
Yes, of course there will always be runway changes, requiring a condensed re-briefing below TOD, but the implication that both or all pilots will be head down, engrossed in the plates and not regularly glancing at their PFD is what I find so difficult to understand about this incident - especially during a significant change such as a level off.
You put the plate down for a moment and watch the automatics capture the new FL and the thrust levers come up, then continue.