Jason, I measured my son's '63 K10 and best I can tell, it measures 77" to the top of the crown at the back of the cab. So it sounds like you might be good to go. I hope you can get your truck in your possession again without an issue.
I think the flatbeds look best with a skirt around them, with or without tool boxes. Something like this
That is what I will be putting on my '66 C30 one of these days. Of course I will be fabbing my own