Considering the labor costs involved to do a "timer" scenario added to the cost of the relevant timers and additional materials, it would more than likely be less expensive to buy the right size generator. Not to mention the reliability issues.
I believe you may need to select a smaller overload relay/contactor configuration to bring the parameters of the protection design more into the middle of the operating current range of the motor. Also, you may have replaced the overload setup with an AB overload which has dip switches on it...