Part of the problem is that there are 140+ advertised trains per hour departing the station (ECS and arrivals into the terminating platforms too) in the peaks and no station with traditional terminating station type boards handles more than 60 departures (Waterloo in the high 50s departures). LBG is on different scale. Most of the users are regulars and the space is designed around capacity.
The "first train to" boards are quite a neat space efficient solution the problem is that there it oftern displays "-" when the platform isn't yet known, what might be useful is to point people to a waiting area near the expected platform e.g. Area A for P1,2
One obvious change i would suggest is that very large platform numbers (6') are put on Lift shafts to help way finding / orientation along with a large LU roundel at the end of the corridor
But if, say, a third of the 140 are inbound to Charing Cross or Cannon Street, then they could be covered by a generic notice like "Platforms X & Y for ...."; and even the northbound Thameslink might be covered by a general "for Blackfriars, ..., St Pancras, and stations north of London, see detailed departure information at .... by access to platforms x, y...[where x. y... are the northbound T/L platforms]". Then a
full departure board for all "southbound" or "away from London" services could be given, and clearly labelled as such, without being unmanageably large. (Providing the two lots of generalised information was prominently displayed along those indicators, so you knew you were only getting one half [ie the southbound half] of the info.)
And if this main departure board was set prominently in the
main concourse you arrive in when accessing the station - with very very clear signs to "departure information boards" from minor access points - at least, that way, there would be "somewhere to start" when you arrive.