Ah right, yes. I didn't study those graphs in that detail - I just saw the "headline" quoted differential. Most of my projects tend to be very low current so I'm glad I ordered 10 of them!
As it turns out, I bit the bullet yesterday and gradually wound up my power supply to 4.2v and the display has been running 24 hours none stop. Makes the whole project a lot easier and I can now even make sensible readings of the true battery voltage.
Thanks for all your comments and suggestions.
If anyone is interested, here's the draft
, not finalized, article on my website. http://vwlowen.co.uk/arduino/camera/camera.htm
There are comments relating to the power supply at the foot of page 3. It's not "live" on my website yet because I've yet to add credits and references.