I had to add the DSP unit, too, but very shortly afterward the radio came with the DSP unit preinstalled. By the time I found that out it was probably too late to ask for a rebate.
As for the synch detector, it doesn't work on mine either. The PDF manual I downloaded a few years ago doesn't even mention the synch detector, so I likely have the wrong version of the PDF manual, although the printed version that I got with the radio does mention it. I'm wondering if the feature was eliminated in later models. The ICF-2010 I used to have In the 1990s had a very effective synch detector, but I no longer have that radio. At any rate, I don't need the feature, as I listen to very few stations in AM mode.