Willair - how would you propose to tile the ceiling?
Ownting - 28 mm Battens and 10 mm pb would be a maximum of 40 mm - is the height that critical? ie already less than 2400mm?
It is super absorbent - it will suck up about 4-5 times more paint than you would expect, and then some.
Simplest solution is use furring channel and screw 10 mm pb to it, run all your cables in the minimal space including the smoke detector.