Jesus was buried by two men, Nicodemus and Joseph of Arimathea. The Bible records that some women were observing the process. There's nothing about anyone being "confused" or anyone doing anything "hurriedly".
What practice are you referring to that "doesn't allowed for anyone to pick up a body, lay it down on a VERY large and flat sheet, and fold it over the body"?
Your "analysis" is rather puzzling to say the least.
The word "wrap" indicates something tight around the body.