As anticipated - today I started placing downlights to test out the best positions to light the stairwell.
After some thought I realised that it was unrealistic to secure scraps of gyprock for mounting the downlights - there is still too much structural work needed to box in some of the volumes under the landings.
Instead I hit on a plan to quickly fabricate some mounting boxes and clamp these in place.
This worked for two of the positions.
For another position it made sense to actually install a piece of gyprock on to the purlins.
For the fourth location I used a bunker light mounted on to a stud.
I hooked up each light using an extension lead and then waited until darkness at the end of the day.
It seems that a single downlight under each landing and floor level will be sufficient to adequately light all of the staircase.