The judge ended up telling them to JFGI [0], since not googling it was costing the city thousands in court fees. That should address your concerns. It probably didn't get me every releasable number, but I'm sure as hell not going to sue and waste another six months. It takes too long to sue, they know it, and it's a huge factor in why this is all so difficult to do.
Please realize that paving the way for others to obtain this data is a huge part of the end goal. In some ways, I'm trying to fix the potholes of FOIA.
[0] "Next, DoIT and its counsel conducted online research on each remaining responsive phone number — in other words,they "googled" each number to determine whether that number was publically listed, and, if so, to whom it belonged."
Edit: Cleaned up (a couple times).
Somewhere in the 9.5 million dollar budget of the Mayor of Chicago [1] they could squeeze out $20k for a HP Records Manager setup (or any of the dozen competing software packages) and just blindly catalogue all emails in to it. Even without setting up ANY of the business classification features it makes this kind of search trivial.
Perhaps it could come out of the 1.4 million dollars allocated to the "Innovation delivery team" who "Creates and implements new solutions to improve the efficiency of City government.".
[1] Page 59 Program and Budget Summaries by Department Finance and Administration Program Summary OFFICE OF THE MAYOR (http://www.cityofchicago.org/content/dam/city/depts/obm/supp...)
The remaining reasons, mainly an inability to filter emails by department, sound normal. If you're designing a database, can you build an efficient index for every possible query? No. The mayor's office has not optimized their records for random people making FOIA requests. Nor should they. I'd rather my tax dollars go to potholes, rather than axe-grinders.
You'll have better luck with more legwork on your end.