I've done countless (well, maybe a couple hundred) air compressors on Soft Starters, it works fine. You will likely end up at about 300-350% Current Limit, (assuming you have one with that capability) and set the ramp time as low as it will go so that it goes into Current Limit immediately. Should get to speed in under 10 seconds that way.
But to the other points, IF it is a bad unloader, the Soft Starter will make things WORSE. So let your customer know in advance that if you put in the Soft Starter and the motor stalls, it was a bad unloaded all along and not your fault. Do compressor people lie about that? You BET they do; they want to blame anything wrong with the compressor on something else.
Get a good soft starter, not a cheap one. The cheap ones only put SCRs on 2 of the phases, the third phase is a piece of bus bar. That is TERRIBLE for the motor, but on light loads like centrifugal pumps you pass though the ramping so fast, nobody notices. On a compressor, it will wreck the motor in short order.