You are hunting very close to where I live and I can assure you I would never carry an 11 lb rifle goat hunting. I have hunted them a lot and even done a bit of guiding for them too and you can almost always stalk them really close. The outfitter I worked for had lots of bow hunters and had a great success rate. Just buy something light and relatively cheap such as a Tikka or something like that and have fun. Rounds in the 260 Rem to 30-06 range will be perfect.
