Elderly Brit here. I would use the English past perfect in both halves of a sentence like "By the time I had finished eating, he had drunk a whole bottle" - when he’s drunk the bottle, I’ve already finished eating, a completed action.
Without wanting to split hairs, is the concept of the French "le temps que" slightly different to "by the time that" or does it just take (to my mind!) a less logical tense?