I didn't open Cliff's response yet, but as a 3gun competitor and not a hunter, I'd start with upgrading your gunshot trauma supplies in your FAK

(2) Israeli bandages or similar compression bandages
Special Forces type self administering tourniquet
Kerlix roll and gauze
hemostatic sponge like Quick Clot
elastic adhering tape like Coban
petroleum gauze to seal chest wound
nasal pharangeal airway
steri strips / crazy glue
betadine
non adherent pads
burn gel
irrigation syringe
good shears like electrician shears not cheap import
dedicated LED light
chem lights attached to a string so can be circled overhead to identify a landing site for helicopter
gloves, and hand sanitizer to protect responder