Based on hood requirements a 1200 cfm exhaust hood would be adequate for a considerable number or size of heat producing appliances. If your HVAC system only produces 1450 cfm (3.6 tons based on 400 cfm/ton)and you are exhausting 3 tons of conditioned air I would first question either the amount of the exhaust air and/or the capacity of the a/c system. Best case you can bring in 80% (960 cfm) make up air and introduce it through a supply plenum in front of the hood and then bring in 20% (240 cfm) through the R/A of the a/c system. Depending on what part of the country you are in this 240 cfm of O/A can be a considerable load to an arleady stretched a/c system.
This is not allowing for any additional infiltration air which must be accounted for. You stand a good chance of running an extremely negative pressure in the house which,
will bring even more O/A. You can also encounter a serious humidity problem.