Ah, I think I’ve found the answer to my own question, so I’ll document it here, in case anyone else searches for something similar.
It seems that ALSA automatically stores the current configuration of the many and various settings it has in a file named /var/lib/alsa/asound.state when the host is shutting down. So, if everything goes OK, you shouldn’t need to programmatically set the volume to a specific level on rebet: it should be done automagically for you.
However, I have found that I can use the following commands to set the volume as I wish:
sudo amixer set Master 90%
sudo amixer set Digital 90%