Writing in generalities, one approach is to provide MUA to the furnaces so they don't get back drafted from negative house pressure. In some cases this can be done by tailor made or factory made hardware directly to the furnaces. In other cases the furnace room would be sealed from having an air path to the kitchen. If possible, which depends on heating type, this would address the safety issue. The VAH flow rate then would be determined by how negative the house pressure got with whatever leakage the house and air conditioning has.

A kitchen MUA could then be added if necessary to get good hood flow. You may want to condition this air. This is the bigger bucks part of the problem. Either furnace hot water has to be diverted to a heat exchanger in the air path (if the heating is hydronic), or electric resistance coils used in the airflow. Adding another furnace for the occasions of high vent flow is overkill because, unlike a restaurant, the periods of high flow would be a small part of a day.

The kitchen MUA has another issue -- normally one wants to filter out critters and bugs and even dust from the air duct, and this causes a pressure drop. In such a case the MUA will not be making up as much air as desired unless a blower is added to the MUA path. Now there has to be a scheme for controlling the blower.

However, if not conditioning or filtering the air is acceptable, then a large duct to a diffuser with a damper controlled by detecting hood air flow is a simple, low-cost solution. Broan makes a unit for this, or DIY using one of many Honeywell motor controlled dampers is an option.

I suggest reading or at least skimming the literature linked at my "my clipings" page. In particular, Greenheck covers the topic well, albeit from a commercial point of view. But the commercial POV is the one that led to the Pro-style ranges and counterpart ventilation systems we are addressing with MUA.

Last, while I think HVAC solutions other than another furnace are options, the more DIY one gets solving MUA the more one is trading one's time versus paying for a slightly more expensive turn-key system. But at the 10K price point, even with a hands-off goal, I would look for other bids/approaches including HVAC companies concentrating on restaurant HVAC systems.

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