With thanks to Radius, I got this working. It’s not the Super Game Boy BIOS which was wrong, but it only seems to be working with v1.0 of the Super Game Boy ROM and not the later revisions or the Super Game Boy 2.
Unfortunately - and I don’t know if this is a bug in v1.0 or the emulation - but Donkey Kong '94 won’t load. I get sound, but just a black screen when it tries to load the borders. Regular GameBoy games work fine (but for those, I prefer to use the gambatte core) and one or two other SGB-enhanced titles also seem to be working, so it’s not that all SGB-enhanced titles are broken.
DK’94 works without any problems using the Super Game Boy 2 ROM in the Stable build.