If you're a member (which I see you're not), there is a great article that includes a downloadable tool for calculating catenary curves. Honestly, for those new to UL, the membership fee is more than worth it. But if that's too much for you, I bet you could find something for free with a simple internet search.
I'd say a big plus one on doing the cat curve though. It was a bit of work on my tarp, but it was totally worth the extra time. I learned a lot more doing it too.
Also, on the beaks, I pitch my tarp high enough that it hasn't been too much of a problem, but I still have Newton's mod in mind in case I get tired of the lower entry some day.