wellygary:

 

Find out which way the beams are going in the space between the floors,  ( removing a roof light fitting usually a good way to have a ferret into the "Roof" space to check this.)

 

Usually you'll have a pretty unimpeded run if you go parallel to the beams and use a fixed wire ( a couple of unbend coat hangers are helpful) to push a drawstring from the edge of the room to whereever you want to mount your AP in the ceiling... 

 

The problem is there's no ethernet anywhere near the ceiling space.