Having read all this, I'm now a bit happier that my monitor has an external PSU. What I'm looking at is running a socket from 12V Molex to the back panel of the PC and supplying the monitor from there. It'd get rid of the brick and also move the PC's PSU in to its efficient band. The PSU is a Seasonic 330W; it runs at 45W input at idle and never more than 120W on full load, so it should be able to supply 3A to the monitor.
I wonder if, with a monitor that has an internal PSU, if it'd be possible to remove the borked PSU and just use the PC's PSU. Not flexible, as the monitor would be linked to the PC, but perhaps a jack socket on the monitor would allow it to be run from a brick instead.