I would not leave it in the sun. It may check. Get it down to near finished bow size. If you are in a huge hurry back it and you could tiller it in 8 days or so. one layer of sinew will cure in 2 weeks or less. 2 layers will take 2 months. Sounds like you just want a quick bow. taking your time will make it better but you can get it shooting in a couple weeks and it will gain a little power over time.