The HRV system is exhausting 150 to 200 cfm of air, which has already been dried to some degree after giving up its heat to the incoming airstream. Someone has suggested using this exhaust as the make-up air for the kitchen range hood. Seems like a good idea to me. I would think one could get decent results with about 150 cfm, though some range hoods are rated 300, 400, even 600cfm. We have a Sakura range hood in our existing house (600cfm). If you need a high-performance range hood without the ridiculous high costs, the Sakura is the best we've found. For about $300, you get a dual fan, dual motor high-performance unit with turbine-style impellors and grease collection at 4 points. Four grease cups to clean, but no filter. It beats the pants off the pretty stainless units costing $1500 or more. We've had ours about 20 years without a single failure in daily use. Make sure you install it with the recommended 7" duct. We do lots of smelly cooking and frying, and I find the range hood never needs to run both fans, it is that powerful. Each fan has two speeds, and it seems running one fan at low speed is adequate for all our cooking. This could be about 150cfm. A lot of the $70 range hoods are running at 60 to 80 cfm.
A duct with a 3-way shutter could be used to redirect the HRV exhaust to the kitchen stove. In the normal position, the shutter directs HRV exhaust air out of the building. In the other position, it directs the air to the kitchen stovetop. I plan to provide a stainless long and narrow rectangular register close to stove-top height on the backsplash. Note the air temperature could possibly be a bit of a heating demand issue. Some way of equalizing the flow rate of this make-up air with the range hood exhaust flow rate is also an issue needing attention. The next challenge is the ducting needs to be valved (shuttered), and an insulated, fire-rated valve may be needed in the grease-laden exhaust terminal at the end of the kitchen range hood duct. (Otherwise air is leaking out of the kitchen range hood all the time) The insulated valve should be electronically controlled and interlocked to the range hood operation (I would think preferably with low-voltage, say 24VAC, to reduce the possibility of sparks in the grease-laden exhaust duct. A hand-operated mechanism with spring return could further reduce the chance of sparks, though I imagine operation may not be as convenient.
One more issue is that we plan to have more than one kitchen in our house. This presents another challenge, assuming the HRV flow rates are indequate for both kitchen range hoods to operate at the same time. - The best option might be to provide a dedicated 2nd earth-tube for the make-up air. another option might be to boost the HRV system flow rate with a booster fan. We've been considering a 2nd earthtube as well, though I think this is extreme - the cost of the earthtube right now seems high -see the coming earth tube article. And the 2nd earthtube would need to be placed far enough from the first to avoid a degradation in soil-to-air heat exchange.