Yup, just like that! ERC with hickory or bamboo have been my best combo's for deep section longbows. When making a R/D bow, though, you need a certain amount, or really ratio, of width to thickness to ensure limb stability. So, don't go too narrow.
ERC is soft but elastic, so it can be pretty thick to start. I'd go, like 5/8"-3/4" on the cedar and 1/8"-3/16" on the ash. You're on your own for width, I'd likely start 1-1/2" minimum, and 2" wide even better. At least until I get more experience with the wood.