How can it be reconciled that the sun will be rolled up and cast into Hell, and that it will draw near to creation on the Day of Resurrection by the measure of a mile?

First: Time in the Afterlife differs from time in this world. The Day of Resurrection is long, with multiple events occurring therein.

Second: The verse, "When the sun is kuwwirat (الشَّمْسُ كُوِّرَتْ)" means the loss of its light, its gathering, its being wrapped up, and its being cast into the Fire. This "takwir" (coiling/folding up) is one of the signs of the Day of Resurrection.

Third: The sun will undergo multiple states on the Day of Resurrection. It will draw near to people during the gathering, and then it will be cast into Hellfire as a torment for its inhabitants. This order is natural given the length of the Day of Resurrection and the changing conditions within it.

Fourth: The "takwir" (coiling/folding up) of the sun mentioned in Surat At-Takwir may be one of the terrors that occur before the Hour and prior to the actual establishment of the Day of Resurrection (between the two blasts), and not necessarily on the Day of Resurrection itself after it has drawn near to the heads of people.

And Allah knows best.