I don’t know, when I wanted to make my sphere I wanted to use readily available barium sulfate powder and an acrylic binder, I never finished it though…

Anyway i’m not saying you should use barium sulfate, but just apply a correction for the paint (as it would be needed as well with BaSO4)

The reference is the incandescent bulb measured outside the sphere, since it emits the same light it every direction, it doesn’t need to be integrated, then you compare the direct vs integrated measurement, calculate the correction factors for each wavelength and apply it when you do color measurements in the sphere.
CT&A doesn’t have a correction function, you’ll have to do it in a spreadsheet or with a script. ArgyllCMS spotread has a correction function.

It’s a private discussion, there isn’t more relevant info to quote.