Another First Timer Studio Build

Good Afternoon. I am in the construction phase of building my first recording studio/mixing room/workout room. The room I plan to utilize is at the back of my shop and since I live in the country, sound isolation is not paramount. I do plan, however, on installing double layers of 5/8” drywall with Green Glue in between. The walls are standard 2x4 studs, concrete floor, and vaulted ceiling. Because of the vaulted ceiling I decided to build a cathedral ceiling at the end of the room where the mixing station will be placed in order to gain some symmetry. Because of this, I have one side of the ceiling that has approximately 59.29 ft.3 of space (if my math is accurate). My question is, should I fill that space with Roxul in an attempt at bass absorption should I just insulate it to match the other side of the ceiling. I do plan on putting bass traps in each corner of the room but thought this might be a good idea for added mass. Another question: Since the building is technically a pole barn, three of my exterior walls and roof are corrugated tin and are separated from the inside wall framing by a few inches. As stated earlier, sound isolation is not a major concern but I also don’t want chirping birds to be evident in all of my mixes. I was thinking that I would just do the 2 inner layers with GG and if that was not enough, I could always tear off and reside the exterior at a later date. I have attached a sketch of my proposed layout as well as pictures of the room. Any advice would be extremely helpful since I was unable to find a similar situation online. Thank you.