Most likely this is simply a "measurement issue" in that you are using a very fast sampling rate on a DMM and have it set to read the highest peak current. What you are encountering is actually not unheard of, it's just rare. There are solutions.
In an induction motor, the 500-600% of FLC is rreally called 'Starting Current", the actual definition of "Inrush" is the MAGNETIC inrush current that happens only for the short instant that it takes to magnetize the windings, BEFORE induction takes place to create impedance and bring it down to the Starting Current level. In that instant, the only thing slowing down the current from being a direct bolted fault is the resistance of the magnet wire in the windings. That instantaneous spike has been know to be as high as 1700% of the motor FLA, depending on design. The duration is very short and most protective devices can't react to it so it is effectively filtered out. But that's not guaranteed, hence the exceptions in 430.52 that allow for setting the instantaneous trips on a circuit breaker that high if demonstrated to be nuisance tripping.
Once we all started going to the newer energy efficient motor designs, it became known that those motors, in the efforts to decrease losses, have even less resistance in the windings and now we are seeing inrush spikes as high as 2200% in certain instances.
So on your pdf, you mention the running amps, but that's irrelevant. A 7-12HP motor will have an FLA of 11A, 1700% of that would be 187A, so seeing 160A or 185A would not be unexpected if your meter can capture a transient that fast. The 200A reading might still be not that uncommon if it is a new motor; 11A x 22 = 242A.
The fact that it is tripping your breakers might be solved by changing the breakers. It's not uncommon that a factory motor starter will use an "MCP", really an Instantaneous Trip (IT) or "Mag-Only" breaker, with the maximum trip setting at 10X the breaker rating (1000%). So if the starter mfr used a IT breaker rated for lets say 15A, the highest setting for the mag trips will be 150A. technically, if you replace those breakers with Thermal-Mag versions of the same make (so the accessories fit), you can go 250% of the motor FLA of 11A, so a max. 25A T-M CB, which will have an adjustable mag setting of 250A. You would not be allowed to set it above 187A, but most likely that will help avoid most of the nuisance trips.
Before going to that extent however, if all 3 motors can start at the same time as mentioned above, that might be a contributing factor and that would be easier and cheaper to fix first. Just make a way to stagger the startup sequence, even if only a fraction of a second apart, i.e. by using an aux of one starter in the Run circuit of another (assuming that works in logic).
