My worry is that if someone turns on the switch in a bathroom with a closed door, the HRV system will just pull the extra air from the other bathrooms, (with open doors) defeating the purpose.
Switching the HRV to high should increase the air extraction from all bathrooms. The bathroom with the closed door should get make-up air from under the door. This is what happens with a traditional bathroom fan.
I'm wondering if the 2 speed HRV is even a wise choice or if placing bath fans in line with the HRV might be a better way to go.
I would certainly consider a 2-speed HRV for a new house. Putting the bath fans in-line with the HRV might be needed if there are really long duct runs from the bathroom to the HRV. In this case, you would need an interlock relay to switch the HRV to high speed when any of the bathroom fans was on, and you would probably also need a one-way damper in the line from each bathroom so the exhaust air from one bathroom doesn't blow back into another bathroom where the bathroom fan is off. I am actually considering doing something like this to retrofit an HRV to my existing house.
I visited a Passive House which uses a continuously operating HRV for heating and cooling as well as ventilation. Surprisingly, they did not provide a manual high-speed control in the bathrooms, but they did have one in the hallway for "high occupancy" mode when you throw a party.
One more thing to consider when using an HRV for bathroom ventilation is what defrost strategy does the HRV use? When the outside air is very cold, the outgoing humid air stream going thru the HRV is cooled below freezing by the cold incoming air. The humidity in the outgoing stale air forms frost in the heat exchanger and can eventually block the air flow.
Possible defrost strategies include:
1. Recirculate for defrosting
2. Shut off fresh incoming air during defost cycle
3. Pre-heat the incoming air above 32F
4. Have 2 alternating heat exchanger cores
If using the HRV to exhaust humid/smelly air from the bathroom, you probably don't want strategy 1. (recirculate) because the stale air from the bathroom would be recirculated back into the house.
Strategy 2 shuts of the incoming air for a few minutes until the heat exchanger warms up from the exhaust air. During this time, the HRV basicly operates like an exhaust fan. This does unbalance the air flow in the house for a few minutes, but exhausting of stale air in maintained.
Strategy 3 pre-warms the incoming air above freezing, which prevents cooling the warm stale exhaust air to the point where frost builds up. This is commonly done with an electric element to pre-warm the incoming air, but the incoming air can also be tempered with a ground water loop with a heat exchanger. I've seen a ground water loop used on a Passive House in Wisconsin to pre-warm the incoming cold fresh air to the HRV in the winter, and to provide the entire cooling for the house in the summer. (No heat pump involved, just 600' of PEX burried 8' deep circulating a water-glycol solution to use the 50F ground temperature for pre-heating in winter and cooling in summer.)
I am not aware of any HRVs that currently use Strategy 4, but I have seen it written up in a paper, and expect it to eventually show up in a commercial product. With alternating heat exchanger cores, one core is active while the other is allowed to warm up letting any accumulated frost melt. Every few minutes, the cores are switched.
For a northern Illinois climate, an HRV using strategy 2 for defrost with high speed controls in each bathroom is probably the most practical solution. You would want to have a stale air pickup in the kitchen (but not too close to the stove) and maybe the laundry/utility room as well as in each bathroom. Fresh air that has been warmed by the HRV can either be ducted directly to each bedroom and living area, or fed into the forced air system ductwork.