On January 2 at 6:21 AM (there's one of those in the morning????), I got a response from Lewis telling me she'd look into it and forwarding the concerns to Councilor Ryan Vaughn, who represents the Broad Ripple area on the council.
I later got an e-mail the evening of January 4 from Adam Collins, one of the administrators within the Department of Code Enforcement. He wrote that normally, taxi complaints require knowing the vehicle's cab number, but they'd still investigate my complaint by asking the company to identify the vehicle or submit all vehicles for inspection. Collins also wrote about some of the process that taxi code enforcement has undergone since DCE's creation, that through 40 random inspections every week, each cab is checked aesthetically at least twice a year and that random mechanical inspections are done weekly.
Collins also wrote that DCE has set up a specific e-mail (firstname.lastname@example.org) and phone number (327-TAXI) for taxi complaints.
Kudos to all involved in this.