Greetings,
I wonder if something like this would work. Maybe in a 4" size or so...
DuraTech 5-inch Chimney
That is a scary looking installation, especially with paper backed fiberglass insulation.
I suggest that you remove it, screw sheet metal to the inside of your framing, add a louvered vent to the exterior wall at the top and bottom of the pipe compartment to vent heat. You can then insulate between the studs with 2 inch foam siding board on the outside of the metal. You may want to modify your framing to make a removable panel as well for future maintenance access.