If there is an H&C train on the terminus platform at Plaistow, is that
likely to leave before any H&C train going westbound leaves from the main
platform?

It's a bit like the Wembley Park problem, knowing which one to take. How
simple would it be to have a dot matrix display before you go down the
stairs, showing which one is leaving first, in these situations? I mean,
this is the 21st century, how hard can it be? and it would make the whole
tube experience so much easier and less stressful for the passengers,
particularly in rush hour.