We've taken what are the clinical standard measures - and some indeed feature counterintuitive questions. And you're right, one of the main issues with 'insomnia' is an unreliable sleep pattern.
We don't want to know how you slept last night, since this may be unrepresentative; but as you say an 'average' may also not capture it/be a natural way to report it. 3 x sample points ('last 3 nights') may be longwinded. Will consider...any ideas on a better question?
Start with "do you go to bed at roughly the same time (within 1-2 hours) most nights?" and only ask the "what time" question if people say yes to the first one.
I no more have a time I go to bed every night than I have a US zip code or a ten-digit cell phone number.