Have done this several times with varried success, based on the weight of the canvas in the tarp. 8 oz. is too light and lose weave to shed water, no matter how much waterproofing you apply (allows a mist to spray through the weave even in light rain). 10 & 12 oz canvas will shed water if you apply a waterproofing agent in addition to what's already in the fabric. Lowes water-seal works well(what they sell for sealing decks and porches).
For real waterproofing go to a 50/50 mixture of linseed oil and mineral spirits. Hang the tarp and paint the mix on, then let it dry in the air for a day or two. This is the PC way to waterproof the fabic and it works well, you can even add color to the mix (yes they did that back then).
I have seen instructions for using bees' wax and parrifin, melting them into the fabric with hot irons. It's still going to cool, harden and crack. I can't imagine it being as good as the linseed method, or as easy. Sounds like a good way to ruin an iron!
For a less PC method, try exterior acrillic paint in a historic shade. The good grades remain flexable enough to last for several uses before flaking, and repainting is a simple process. In spite of all their PC talk, a lot of the re-enactors at the major historic sites use arcrillic paint on their canvas while poo-pooing other peoples' gear. Stick with brown, rust red or dull yellow, these are all historic colors.
I have seen properly set up diamond shelters maintain a 50- 70 degree temp when the outside air was in the 20 degree range (small fire and a reflector, straw around the base).
How big were the origional diamond shelters, are they PC? Who Knows! Who gives a rat's A$$(and I'm a thread counter!). They had a cover on every pack saddle in the string! That's what a diamond shelter represents, a wagon or packsaddle cover!!! They might not have been exactly square, but they made good shelters. If you want to be totally PC limit your camp gear to what you could have carried on one horse wraped in the pack cover you use as a shelter!
Your improvised shelter is more historically accurate, and WAAAY cheaper than a hunter tent or baker and will jury in at any historic site in the nation. I have slept through many heavy rains in a good diamond. Right now I own two wall tents, three wedges, a 10X10 one pole and still keep 12X12, 10X10 and 8X8 diamond shelters on hand as well as assorted tarps of other sizes. You never have enough knives, guns or tents. I reciently had to clothe and shelter 25 visitors to a PC wedding, and didn't have to buy a single item!
Don't consider your shoe string budgets a hinderance, but a reality of the frontier. Most of our ancestors were not well off and had to make do with what was available. Research what they had and how they used it. Remember, there were 100 Leman and Henry trade guns for every Hawkin, and a thousand smoothbore trade guns for every Dickert or Rupp. Their hand made knives usually looked like pieces of manure,not works of art, and manufactured butcher knives were imported by the hundred gross!