Not to mention the fact that if I want to cook it again, I will have to clean out the used charcoal.

If it were mine, I would do all of the following before shelling out money for a secondary system.Check ther attic insulation.Consider installing UV heat repelant tint (it has a service life) on all sun side windows.Have a thermo scan done of the exterior and interior to see where heat problems occur.Have the AC system check by a tech for proper amount of coolant, and to see if its too big or too small.Vent the cooking hood outdoors (if it's legal to do so).Install ceiling fans in the hallway upstairs and in the bedrooms.Have tech make sure the draw air system is sized (and positioned) correctly for each floor.Make sure the thermostat is not a (NASA Project of complication designed to micro manage the temp), and that it is working correctly.Some Techs are much better than others....Good Luck!

In general, the main issues that come up with city regs are adding a full kitchen (stove/cook=top), completely separating the units with a wall vs a door, and not having egress windows (big safety/liability hazard). 

No vegetation, roots along foundation.

Does anyone have any recommendations for reasonably priced tax appeal services for Cook county?

Hate to tell you this but back in Aussie a Swede is a root vegetable we put in stews.

I am specifically interested in the western suburbs within Cook County and DuPage – Areas like Berwyn, La Grange, Westmont, Lemont, Naperville, Glen Ellyn, Elmhurst, ETC.

I purchased in the 2019 Cook County Scavenger sale How did you finance this deal?

Quote from @Jonathan Cooke: Allow me to play the devil's advocate since nobody else is chiming in.You want to borrow money to borrow money, thinking a shortcut will make you wealthy.

These are all off market properties and are located all over Cook County.