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If the monitor (or any other load, for that matter), is functioning correctly, you cannot have "too much" amperage (current). The load will only draw as much current as it needs, despite the battery being able to supply more.
BTW, can someone translate "wall wort" to Australian English?? I think you mean a socket outlet, but I'm not sure... And is it 12V AC, or DC?
EDIT: I think I realise... a small DC plugin supply.
I suggest a 12V zener voltage regulator should be put before the display because in case the battery is full charged the terminal voltage tend to go slightly beyond 12V which may damage your LCD circuitry if it is not protected already.