Really ... you're really going to pursue this?
I would suggest that 'early' on any day, 'while it is still dark' suggests the morning. Ity's clearly not the eventing, is it?
But, because I wondered how Hart translated other texts – such as Luke 24:1:
"But on the first day of the week, in the deep dawnlight ... " whereas the KJV has:
"And on the first day of the week, very early in the morning ...
(The Greek phrase is ὄρθρου βαθέοςis, orthros bathos – orthros (daybreak, dawn, early in the morning), bathos (literally – 'deep', figuratively 'very early').
Mark 16:2:
"And very early on the first day of the Sabbath-week they come to the tomb, as the sun is rising... "
Matthew 28:1:
"But after the Sabbath, at the dawn of the first day of the Sabbath-week ..."