Um! I thought I wouldn't be able to wake up, but I did, so that was ok. I started the test at 22:27 on 4.6. Set the alarm and tested at 00:27 (How did I manage that?) on 4.7. Set the alarm and tested at 02:27 (!) on 3.7. Abandoned the basal test and ate 3 glucose tablets.
Maybe not that successful, but it felt like a milestone to me! I'm now going to do the basal test 2 or 3 more times. If I can rule out the Basal as the problem, I can then look at the accuracy of my Bolus ratios or of my carb counting.
There's another possibility: I have a feeling that my basal is running out at around 04:00. I don't split my Lantus at present. The difference now is that I could go to a HCP with more confidence and
weigh up advice instead of reacting blindly with no real understanding of why!
Again, thank you to all for advice and encouragement, and especially to
@noblehead who advised me a while ago on how to test. Your advice did eventually get through to this slow learner.