Your meter will do both 100ms and 1ms ranges in min/max recording mode. Which are you using?
At 100ms the interval is 6 engine revolutions, a gaseous fueled engine may not be able to respond substantially to the throttle in that time under ideal conditions. At 1ms, there is no chance at all.
If you are getting only a flicker down to 176V when the AC starts, my guess is that it has probably always done so, and you are noting it now because you have decided to do "an extended run to load test". (other times when your generator is actually needed, you may distracted by other concerns and perhaps less critical)
I have a 15kw diesel set and my HVAC is 2.5T; I have never measured the instantaneous voltage drop when the compressor starts, but flicker is somewhat more noticable when on the generator than utility power. I call it normal, since a 15kw genset has a fraction of the momentary current capacity of the 15Kva service transformer that normally feeds my house.
This is becoming a trend my agreeing with Mastr, may be it will soon end but for now...... I think you have a normal situation. If your A/C unit has some age on it it will take a little more to start it than when it was new. The start/run capacitors will weaken over time and it will take a little more to start the compressor. The gen. cannot compensate for the start up inrush as quickly as a utility transformer. The transformer is a continuous supply going from ( on the low side) 4160v/240v where the gen. is straight 240v.
I have 40Kw diesel units that will "burp" when the A/C unit starts but there is no problem. For now you don't have a problem with the unit and are experiencing a normal situation.