Thank you for the explanation. I see that native speakers have the same opinion as yours:
What is do think about the word combination "already almost" in other situations? Do the next examples sound natural for you?
It is already almost impossible to find savings rates that beat inflation ...
Joel is already almost asleep.
And there are examples of "already almost dark/night" in some books. Are they old-fashioned?
It was terribly cold; it snowed and was already almost dark ...