There is zero chance that I will have a larger bathroom, it implies moving house inside Amsterdam which is virtually impossible with the current crazy housing market. And even if it came true, it will be my girlfriend’s domain, not mine, my hobby is doomed to be restricted to the dark corner behind the cupboard.
Painting with latex may make a styrofoam sphere a bit more heat-resistent. I experimented with a PVA-bariumsulphate mixture too (PVA=polyvinylalcohol), that handles a bit better even and should give a better (more constant reflectivity over all visible wavelengths) coating too.
But there is no other reason to start with a styrofoam ball than easy availability, if you can find a sphere from any other material and give it a flat white coating on the inside, you are good. I hope to find an affordable nice metal sphere at some point, that should handle any output power.
It is a misconception that input-output efficiency plays a direct role in integrating spheres. It does not matter if the sensor picks up only a tiny fraction of the input power (which indeed it only does), it can be any fraction as long as that fraction is the same for all colours and output directions of the light source. Your multiplication factor then takes care of the correct calibration. The only reason that you want high reflectance on the inside of your sphere is indirect: high reflectance causes more reflections before the light is finally lost or reached the sensor, and more reflections equals better integration.
(As a side note: I suspect that most people on BLF have no idea what light integration is, and even if they have a clue, why it is an important feature of your device in order to measure light output. I hoped that my threads on integrating spheres would help a bit but it does not seem so.)