I can't speak to this specific model, but the (few) ink-jet printers that I've seen have a 'cartridge change' procedure.
"... it always reverts to its 'home' position and the cartridges are concealed beneath the casing. ... Do I really have to take the casing off to do it? "
I very much doubt it.
"How can I fool the machine into thinking it needs a cartridge change?"
Generally, you will 'tell' it that it has a new cartridge.
Do you have the Installation Manual (or similar title) that came with the printer? Does your system have the Epson support programs installed? If so, there may be instructions somewhere embedded within the menus. In Windows one would get to it via Start > All Programs > [probably]Epson.
Start at
http://www.epson.com/, and navigate your way (Europe > UK: right column, low > Drivers & Support). I don't find the 840 listed. But for the Model '800+',
these instructions MAY give you a clue.
If this doesn't quite fit, check the instructions for other models to give you a flavor of how this manufacturer generally designed for serviceability in it's products.
UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8.0.9) Gecko/20061206 Firefox/1.5.0.9