Even with the Calibre's dismal performance it'd probably have gone off before you met the officer, at least if he'd targeted your vehicle while approaching. But from your description he clearly used his rear antenna and popped you after you'd passed by.
Depending upon these targets' radar cross sections and the relative proximity of the three in relation to the police vehicle, yours was probably the strongest target. But you can probably answer that question better than I: was the cited speed close to what you were doing? I'd guess that it probably was.
As for questioning in court the radar's accuracy, don't waste your time unless there was obvious evidence of operator error, which doesn't appear to be the case here. And one question you may care to ask yourself: "How could I possibly have failed to react to a passing unmarked police vehicle?" From the description, you apparently continued driving in excess of the limit even after passing him, reacting only after the Calibre's belated warning.
Sorry I can't offer much hope. But you may get lucky; the officer may not appear in court.