I'll comment on your calcs.
At first I thought it was incorrect because of the Istart = 3* Inom, then I realized you were calculating the starting at Y-Delta. Although this looks good on paper, the reality is, Star-Delta is not what it appears to be, it's kind of a cheat. The INITIAL current is reduced when in star to being 300% of normal, but when it transitions from Star to Delta, there is a second current surge that will in all likelihood still be as high as 600%, sometimes WORSE if the conditions are right (wrong). The only real difference between DOL and Star-Delta starting in my opinion is the length of time that the current is high, being that with S-D the motor is already moving so the second surge is of comparatively short duration. If your generator cannot handle that second hit, you will still see flicker, or worse yet, trip the generator main breaker. For this reason alone, you will rarely see Star-Delta recommended as a starting method behind small generator supplied systems.
If you are fearful of the idea of using electronics such as a VFD or Soft Starter, a Reduced Voltage AutoTransformer type starter would be a better choice. Because of the transformer action, line current is much lower compared to other starting methods. If the motor will start with S-D, it will likely start at 65% taps on the RVAT, it may even start at 50%. It's still a two step process, but if you use what's called a Closed Transition (Korndorfer) starter, you will not have that 2nd high peak. 7.5kW is pretty small for an RVAT starter however, you would likely have to build your own. I would go with a soft starter or VFD rather than go to that trouble.
Take a look at this website from Caterpillar though, it's a good quick way to look at sizing generators for motor starting. It gets more complicated for your situation, but basically if you apply these rules to being for your REMAINING capacity above and beyond the static existing load, you will see that it is not likely that your situation will work.
By the way, I don't necessarily agree with their assessment of over sizing the generator by 250% for a VFD, but the VFDs need other careful considerations, so I'm thinking they are assuming the worst case here and covering themselves for someone who may apply one without proper engineering.
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