Thank you for your replies, but none was quite specific about the boundary-line.
I asked Alex Burton, who has supervised tens of thousands of fasts. He says that the cutoff point is 40. He will normally terminate the fast then, and it also the point at which hospitals will administer intravenous glucose. However, on rare occasions, and with some qualms, he has tolerated a transient BSL of 34 or even 30.
Caution: Home meters are not always reliable at this level. At least, I know my Caresens is not - consistently giving wildly inaccurate readings of 36 where the correct reading is 45.