Hey,
I believe the amstrad CTM644 has a variable resistor on the pcb for this...
Open up the back of the monitor. On the PCB there should be a variable resistor call "SUB-BRIGHT" or "BRIGHT-SUB" or something. Can't remember which way to turn it, but make sure the external "brightness" control is at max when you set this. Can't remember which way to turn it.
Of course, if the caps are knackered then this may not help much, but you may be able to squeeze some more juice from it.
The only other thing I can think of is Voltage levels.... I know the amstrad used an 8-pin din socket, but I'm not sure what voltage levels it was expecting (0.7V/1V/5v etc...).
Hmmm a rather cheeky (and no doubt someone will say why its a bad idea) idea is that you could un-terminate the video signal (inducing a fault where the picture is really bright) and then lower the brightness to your liking with the internal pot..... This may not work though, depending on the range of the pot.