IF you decide to use a piece of cloth for a shelter, set it up as a simple leanto, or as an open-ended wedge tent. Those two styles are well documented.
That "diamond fly" or "plow point tent" are not documented at any time before the very very late 1800's and early 1900's. Yes, the Diamond Fly has become .... accepted ... almost universally for "longhunters" - even at juried events. Yet documentation for it just has not been found. Lots of people have searched, but still haven't found it.
So the ... longhunter culture ... that has evolved has clasped the diamond fly/shelter to their bussom and run with it. Ditto their folding handled skillets and corn boilers.
This all assumes that you want to do an accurate historical interpretation. But, in the end, it is all a matter of personal choice. So choose what will work for you.
Mikey