This is where you have to have a sensible discussion with the architect and client, with a bit of practice you will learn to steer them in the direction of making a sensible alteration to the plan.
I have been faced with near enough the same problem with exposed beams in the past, I have used two different solutions to it in different cases.
1 - have the infills between the joist battened down to create a small void above and notch the joists. steel plates can then be fitted over the notches to protect the cables.
2 - have a boxing made of the same wood and height as the main beam which fits against the wall covering the ends of the joists and looks like another beam sitting on top of the wall and holding the ends of the joists. This 'false beam' will look like part of the structure and give you a nice void to hide your cables in.
To encourge architects and clients the phrase 'this would add to the aesthetic' can be quite useful!