using the M1 should work fine as a startup/shutdown controller, but I don't think it has enough power on the +12v rail to power the EeePC and a monitor. the total wattage of the PSU doesn't matter, each power rail has it's own maximum output (power cannot be shifted from rail to rail).
the M1-ATX can only provide 2A MAX on the +12v rail. the eeePC's AC home charger outputs email@example.comA. most small LCD monitors use around 10w (12v@~.8A). that brings your 12v power draw to roughly 3.1A which is too much for the M1.
the M2-ATX can provide 7A on the 12v rail, so that should be able to handle everything no problem. otherwise you can power the EeePC's car charger from an external 12vdc source (car battery, cig lighter socket, etc) and use the M1 as a 5v power supply and a system startup/shutdown controller.
another option is to buy a separate startup/shutdown controller and a separate 5v point-of-load (POL) power supply. you can power the computer and monitor from the car's 12v, and the HDD and USB hub from a POL.