I'd be a little leary of how well a canvas tarp would work for a hay cover. Just thinking out loud,, would you put a cotton blanket over a hay stack and expect it to keep the moisture (rain) off the hay?  The poly tarps found at local farm type stores are little better. I'm talking the $1.295 variety you can read the paper thru.

The tarps used around 'here' have a silver/black/blue coating on one side. Yes, they're more expensive. If you can get the tarp down below the pallets like a tent, and leave the end's open for air flow,, think you would keep the hay dryer.

I'm not in N.Y. so don't know what your residual humidity conditions are, or how much wind you get??  If you can leave/make some  "breathing room" it would be easier to keep the moisture out of the hay.

'Here' tarps have to be tied down tight to the stacks. Wind has a nasty habit of ripping tarps off stacks if the tarps aren't basically "superglued" to the stack.  Fortunately we have very low humidity.