And then the mounting bracket will fit. It even fits well.
After all the soldering, the actual installation was mostly anticlimactic, other than the placement of the external microphone.
Tomorrow, I'll see how it works with my iPod. (One of the requirements for the radio was that it have a front USB port and a front AUX in. The fact that it comes with a real volume knob and real buttons is a bonus. :) )