I opened a bug report for the problem (have a look at the related posts below) and got the response that it is a problem in pstoraster. This means it is a problem in ghostscript, not in CUPS.
So I had a look at pstoraster and seen that CUPS_FONTPATH is added to GS_LIB. Theoretically it should solve my issue when I set CUPS_FONTPATH, but this assumes I can do it without CUPS discarding my settings.
Unfortunately this assumption is not true. I tried it and I still see the same behavior as before.