Black screen when trying to boot into recovery mode
I've got an older MBP that I haven't booted in a while that I want to give someone new to use. However, I cannot remember the password and the version of MacOS on it (I think Mohave) does not offer any options on too many failed attempts (e.g. Apple ID authentication).
Because there isn't anything I care about on the machine, I figured I would just boot to recovery mode and do a fresh install. However, all attempts to boot into recovery mode result in a black screen starting about halfway on the progress bar. The machine is alive in there, as I can fill up the keyboard buffer with repeated entry and get beeps, but the screen remains blank. Meanwhile, the machine boots fine to the normal login screen. I've reset the usual SMC and NVRAM already, although hard to imagine that's the problem when the machine boots normally otherwise.
So... I'm well and truly stuck. Ideas I have missed?