Looking for input on insulating a small area of exterior gable wall. 

It is peaked in the middle, 16 ft wide and 4 ft high at center, 2×4 jack studs and stucco exterior. Black stucco paper on the inside of stucco. Gable vent at very peak about 4 in x 12 in

There will be a full length soffit under this gable extending horizontally 26 inches out just for can lighting over a counter then this soffit goes up to vaulted ceiling. Therefore, I can also insulate that soffit ceiling and the vertical interior wall above soffit which i plan to do with R-13/R-19

This is near an airport……So California near the beach – LAX airport…hence I would like to make it quiet more than worry about thermal performance. Just don’t want to use a product not proper for the space (like rockwool safe n sound which is for interior walls), don’t know much about which products might create a condensation type of issue, don’t want to use kraft paper where i shouldn’t, etc

I will have plenty of 4.5 inch thick rigid foam left over, as well as kraft faced R-19 for ceiling (johns manville)

Question is then – how to treat the exterior between the 2×4 jacks? Rigid foam against the paper/stucco exterior wall? Fiberglass batts against paper/stucco exterior wall?Nothing there, just go with insulating the soffit interior with fiberglass batts?