I am an electrician an I am not sure of what this means, (I have a Trane heat pump with a 1/3 starting motor on the compressor.) I think what is happening is when you you go to start your largest load and you have only a few lights on and the tractor govenor is getting caught with ( its pants down ). The fuel rack is delivering the rpms but not enough fuel at the moment to hold the load. This is called speed droop. With your present equipment there is nothing that can be done. Now new on the market is something called a ( Soft Start ). This is a across the line starting device but it slows down the inrush current for a time that is choosen to bring the motor up to speed. They are an electronic ( chopper ,or SCR ) device. A VFD is a Variable Frequency Drive which is a much more costly animal that you do not need. The ( Soft Start ) is a dumbed down version of the VFD.
The motors I look after for my employeer are 2000HP at 5000 V 3 phase. They have been upgraded to soft starts from the older reduced voltage start. Under the older reduced voltage start you could actually feel the building pull down . We have and with out counting because some new ones are being added 20 at 2000 HP each.
I spend the rest of my time with 600 V VFD's. I would guess the Soft Start to $400.00 as the 10 HP VFD I finished last week was $2400.00 and I then placed an order for another to replace on older drive before it blows.
If you adjust the Soft Start to ramp in over 3 seconds which is a very common factory default it will let the tractor know somthing is coming on line, the delay can lengthened to maybe 10 seconds max but you need to play.
You can check out the major brands on line .
Craig clayton