You mentioned exhaust fans. Where is the makeup air coming from that these fans need to exhaust?
I ask because in one commercial kitchen I used a packaged a/c unit to do double duty of makeup air and air conditioning. It could be either 100% outside air and sized for the cfm needed by the exhaust fans OR you can install it with dampers and a control system on the return side to modulate from 0 - 100% air from kitchen to be able to use it when the fans aren't on.
Use the biggest hammer you like, pounding a square peg into a round hole does not equal a proper fit.