She is quite stunning!
Since I cannot have my tops quilted by someone else (because I can't claim them as my own if someone else works on them) I can't answer you LA questions. Pretty sure that the sleeve and any embellishments go on after quilting.
So is the only reason you aren't quilting it yourself because you are not experienced in FMQ? How about taking some Craftsy classes and learning how to? You could put this piece aside and quilt it later when you are more confident. This size is definitely manageable on a regular sewing machine. And there is NO rule that says you have to finish something before starting the next. (Or we wouldn't need the UFO thread on the QB)