I'm pretty sure Best makes one with baffles - don't get mesh. Also look at Kobe hoods - good value. If you're going to get a hood over 600 CFM you need to think about makeup air.

I agree that I don't want mesh, but the only Best hoods that I can find with baffle filters are canopy-style hoods. It looks like all of their chimney-style hoods have mesh filters. I would love to find out that I am wrong about this.

Any advice about make-up air? I understand the concept, but I'm not sure how to implement this. Does it matter if the kitchen is somewhat open to the rest of the house?

Being in Chicago, I'd guess that make-up air is required in your area for venting >600cfm but that's just a guess. Being open or not to the rest of the house isn't the issue. The issue is how air tight your house is and being in a climate zone where there is a wide range of temps throughout the year, it's likely most houses are very air/weather tight. When you suck out 1200cfm of air from an enclosed space (i.e. your house) the pressure difference between inside and out will cause air to try to get in from where ever it can. That means chimneys, water heater, and furnace flues. That's dangerous because the gasses those flues are supposed to vent get sucked back in.

In areas with cold winters, the make-up air might need to be an active system where it gets heated on the way in. This translates to significant cost that needs to be accounted for. You need to consult an HVAC person to get the details. Most contractors don't deal with HVAC other than to provide supporting structure and electrical.

Great. Thanks very much. Luckily (!?) we are also installing a new AC system at the same time, so we're already talking with HVAC people.