I just had another thought. You said you're looking for something to use if you get caught in a rain storm. Many tents now have a "quick pitch" option using just the poles and fly, or maybe the poles, fly, and footprint. Would that serve your needs? If so, you wouldn't need the extra tarp.

I've used the quick-pitch feature with my Hubba tent a couple of times to make a lunchtime shelter when it was raining; I've set my Carbon Reflex up that way once or twice in the backyard, and it seems to work, too.