Late to the thread.
I have been covering pup for 10 years in Chicago area weather. I use a tarp. However, I cut 2x4's the width of the roof and placed 4 of them on the roof, larger side down. That 1.5 inch gap appears to be fine for putting an inexpensive tarp over.If you go this route, cut the 2x4's so they overlap the edges of the roof, so you're not concentrating (eventual) snow load in the center.
Also, as others stated, I go down the sides of the pup with the tarp, but don't 'wrap' it. I use bungees, or often, twine, to put into the grommets and tie the tarp to the frame.
I've had no moisture issues from doing this for a decade. I have cleared snow off the roof in really heavy snowstorms.
And, if no one has mentioned it, you don't store the pup for a season level as you would in camping. Have it slope one way or the other a couple of inches.