I agree that the choice of the benzodiazepine should be conditioned on 1) the time to onset of action and 2) if possible, it being an anticonvulsant.
That said, the doses that the PPeH and the American Clinicians' Academy for Medical Aid in Dying (ACAMAID) call for — respectively 500mg or 1g diazepam — are so large that I expect they would put one to sleep very quickly, as soon as they start being absorbed from the gut.
According to the ACAMAID's data, the average time to sleep is less than 8 minutes with their 5 drug lethal mixture (100mg digoxin, 1g diazepam, 15g morphine, 8g amitriptyline and 5g phenobarbital). It is of course difficult to tease out the effect of diazepam on inducing sleep from the other drugs, but since digoxin is not sedative (it can be taken 30 minutes before the other drugs) and since
morphine delays gastric emptying, it could be that the time to sleep with SN + metoclopramide + diazepam is short too — maybe 10-15 minutes. We need more data on this.
Note that the PPeH calls for either diazepam or oxazepam but the latter has a slow onset of action, so in my view it should be avoided.
I disagree that the duration of action / elimination half-life of the benzodiazepine is not important. We do not have any evidence on the time to death with SN so, in my view, it is important to use a longer acting benzodiazepine to make sure that one does not wake up or have a rebound seizure when the benzodiazepine wears off. Diazepam and clonazepam, in this order, would be the best bets.
Finally, because of the above, it is counteproductive to take propanolol with SN: see
this post and the ones that follow.